She valiantly drove in her car to rescue me, made me coffee in her Edinburgh flat, delivered some fighting talk about changing the Conservative Party in Scotland - and came out as gay for the first time in public. Aware it would be published in The Herald, she freely referred to her then live-in partner - a Green vegetarian - as "the missus" and described their life together. She'd recently quit her career as a BBC Scotland radio presenter in order to "get more involved" in politics, and her enthusiasm and warmth were catching.
That was four years ago, when the former Territorial Army (now Army Reservist) signaller was running the then party leader Annabel Goldie's private office and preparing, aged 32, to fight the 2011 Scottish elections both as a constituency candidate and as number two on the Glasgow regional list. It was said that to survive in Scotland the party needed an urgent transfusion of fresh blood like Davidson's (young, gay and working-class); but she'd just come second on the Glasgow list, giving her only an outside chance.
And look what happened. Davidson was elected regional MSP for Glasgow Kelvin in May 2011 and became party leader that November, following Goldie's resignation. To say her political career has been anything other than meteoric would be like suggesting Edinburgh's pandas aren't cute.
Davidson has taken her place in the historic triptych of female party politicians at the front line of the independence debate. At 35, she's also the youngest and, arguably, has the toughest battle on her hands: the Scottish Conservatives control 15 of the Scottish Parliament's 129 seats and the party, with around 10,000 members, is the smallest of the three. She has been working with Scottish Labour leader Johann Lamont to persuade voters to retain the Union.
Our second interview is, then, more charged. With just weeks to go before the Referendum, we meet in a busy Edinburgh bistro and she has her media director in tow. But in she strolls, dressed in boots, jeans and casual pink shirt, wearing no make-up and stifling a yawn. "Sorry, but I was burning the midnight oil last night," she grins, ordering her habitual Diet Coke. "Anyway, it's an admin day at the office." Her conviviality is undiminished; loud laughter is to punctuate our interview.
It turns out she was having dinner with her new girlfriend of five months. This time around she's unwilling to divulge much detail, other than that her new love is Irish and works for an environmental charity. They first met eight years ago through their respective partners "and out of the blue we kind of caught up again". "In February. So it's early days." She's particularly unforthcoming because she finds it unfair that her private life is under closer scrutiny than that of her married, straight opponents. "I'm not being spiky, but it does get quite tiresome. All I'd ask for is a bit of parity," she sighs. A practising Christian and former Sunday school teacher who was brought up in a strict Presbyterian household in Fife, she and her sister were encouraged not to be "showy"; she once found it difficult to speak about her faith and her sexuality in public even though she has always been open about them.
All that has changed. Being the only openly lesbian in the chamber appears to give her the edge when courting younger Conservatives, for whom issues like homosexuality and same-sex marriage are not the anathema they might be for the older generation. Earlier this year, Davidson wrote a moving essay for the Sunday Herald after the passing of the Marriage and Civil Partnerships (Scotland) Act, for which she had actively campaigned. In it she expressed her joy that the Scottish Parliament had "shown maturity, courage and care" as it sought to extend the rights of individuals while protecting freedom of religion. The bill mattered, she wrote, because the stigma of being gay, lesbian, bisexual or transgendered still existed. Schoolchildren who were suffering homophobic bullying could walk taller into the playground, knowing that Holyrood had stood up for them.
She says now: "The flood of emails I got after I became leader, mostly from boys but also girls, saying they never thought politics was for them, that they realised they could be in the party after all, was incredible. Maybe it's that Presbyterian thing, but I never thought of myself as a role model or someone people would look up to, ever. I was overwhelmed."
Is it possible for a politician to be all things to all men (and women)? "One thing I Iearned as a journalist is that people can smell inauthenticity a mile away. I believe I'm as open as I can be about my life, faith and politics. Love me or loathe me, this is who I am and this is who you get."
It's how to attract the elusive female vote, however, that has been exercising both sides of the current debate. Why have polls consistently found women to be less likely than men to indicate they will vote Yes? Davidson loathes "lazy categorisation". "Women are a fragmented and diverse group. So we've got to be careful." On the other hand, she reckons men are more likely than women to take a punt. Research into gambling habits indicates that "proportionately more men will put out money in betting shops or online than women", she asserts. What is clear is that women are "not buying Alex Salmond's dodgy chat-up lines".
"Women want some sort of certainty; they want to know what they're getting. If they don't, they're less likely to give themselves over to something," she asserts.
Maybe it's simply that women are less interested in politics. "Now, that I will take issue with, because it's not true," she says. "There are large numbers of women who are very, very interested in some form of politics, but not always the cut-and-thrust of party politics. They're interested in campaigns about their community, social justice, female genital mutilation, rape as a weapon of war, schools ... So the challenge is how we make sure women don't count themselves out from getting involved."
Scottish Labour has 18 women MSPs out of 38; the SNP 17 out of 65, and the Scottish Conservatives six out of 15. Can female politicians help encourage women to vote, or consider a careeer in politics? "There are far more women in the Scottish Parliament now, though we could still do more to get better representation," she says. Bringing ordinary women into Parliament to show it's not all that "macho nonsense" of screaming at each other across the chamber can help. "A lot of women don't like the idea of adversarial politics, that you have to put on some sort of armour, a hardened crust, to get heard. I want them to see all the hard work that's going on in getting bills amended and passed, to see that people in different parties like each other and socialise together."
Is she friends with Sturgeon and Lamont? "There are loads of similarities between us, and I like and rate both of them. But because of the roles we have to inhabit it is difficult to be the kind of friends where you'd go out and have glasses of wine and pizzas together - though at the moment I do have to spend more time with Johann than Nicola, as you may imagine."
She claims not to have seen last February's infamous Scottish Television live referendum debate between the two, variously labelled a "catfight" and a "stairheid rammy". "But on Twitter next morning there were some very unsavoury, unflattering comments that would not have been posted had it been two men going at it hammer and tongs."
Nor, presumably, would a certain tabloid newspaper have run a "Downing Street catwalk" feature analysing the men's outfits, as it did the female Conservative MPs' after the recent Westminster cabinet reshuffle? "That's awful. You really would hope newspapers were beyond that."
The unmanned cameras in the Holyrood debating chamber mean women politicians need to dress carefully for First Minister's Questions every Thursday. "The pictures you see on telly are from those cameras. They never move and as women are generally shorter than men, the angle they look down on you can be much steeper and can end up looking down there [the cleavage]. It's silly things like that that women have to consider. I've never been part of the short skirts and push-up bra brigade, and I dress reasonably conservatively anyway. You can wear something indecorous to the pub, but you can't do it for the cameras. I do like a bit of glam, a bit of spangle, but suits have to be the uniform for men and women politicians."
She's had her share of unflattering comments on social media. "I've been called a murderer, a liar, a traitor, a quisling and accused of not possibly understanding what a family is. It's water off a duck's back now but I get quite outraged on others' behalf if they are ordinary people. I don't call much stuff out when it's about me; I do if it's viciously homophobic, because quite a lot of people who follow me on Twitter are gay and they have to believe that's OK."
But she does feel "that sort of nuttery" has died down a bit and is not representative of the vast majority of Scots. "I don't believe Scotland is homophobic or misogynistic. I genuinely believe the independence campaign has been a fantastic thing. Women are engaging, and it's on both sides of the debate."
Asked if she has undergone leadership training, she says she'd had the best in the world - from the British Army. With it came an appreciation of the power of decision-making. Properly researching an issue, then setting out clearly what one is doing, and why, helps defend any decision made.
So that's what women will do closer to September 18? Uproarious laughter again. "Many now see the debate as white noise and have tuned out but will come back to it closer to the vote. We have to be ready for that."