The win, alongside the hosts' second seven-goal haul in four days, took the home side three points clear of Sweden.
"I couldn't have asked for a better start to the World Cup qualifiers," said Anna Signeul, Scotland's head coach. "Scoring 14 goals in the first two games, from so many different players, has exceeded even my expectations.
"If somebody had asked me to take a 3-0 win before the game I would have. We have put seven goals past a team which doesn't normally lose many and also kept a clean sheet. We started the game at a furious tempo and the first 15-20 minutes, especially, were excellent. Despite this great start we won't take anything for granted."
The Bosnians, cheered on by a small but vocal band of supporters, briefly looked as if they might make a game of it in the opening few minutes but that proved to be an illusion. Once the Scots got into their stride the opening period was played largely in the visitors' half.
That meant a torrid 45 minutes for Nikolina Dijakovic, Bosnia's right-back who time and again was left floundering by the pace of Lisa Evans. The Potsdam player was also the scorer of Scotland's first goal, running on to a fine pass from Megan Sneddon and beating Almina Hodzic in the Bosnia goal.
Five minutes later, like an echo of the opening period against the Faroe Islands just four days earlier, the Scots were 2-0 up. Glasgow City's Leanne Ross scored a quick double in Torshavn and she got back on the scoresheet last night when she rifled the ball into the net following another good move which involved each of Hayley Lauder, Evans and Kim Little.
The goal seemed to leave Bosnia overwrought, even that early as the visitors were opened up time and again by the home team's quick passing and movement. Evans had the ball in the net twice more, but both efforts were ruled offside and it was left to Little to score Scotland's third of an excellent opening 45 minutes. The Scotland midfielder exchanged passes with Jane Ross before then rounding Hodzic.
There was no respite for the Bosnians at the start of the second half either as they fell further behind, this time to a header from Rachel Corsie. Seconds earlier the central defender had forced Hodzic to turn her header round a post for a corner, but when Little sent a cross into the penalty area, Corsie outjumped the defence once more to score off a post.
The fifth goal arrived eight minutes later and once again the outstanding Evans was heavily involved. She raced into the Bosnia box and might have had a shot herself only to square the ball to Jane Ross instead, with the striker duly turning to fire a shot high into the net.
A free-kick to Scotland, taken by Little, provided the sixth goal for the home side, with Amira Spahic, the Bosnian central defender, flicking a header past her own goalkeeper under pressure from Jenny Beattie. Almost inevitably the pace of the game dropped and it took until stoppage time for the seventh goal to arrive, with substitute Suzanne Lappin the scorer.
"We've set our expectations high and this has been a great start to qualifying," said Evans afterwards. "We want to make the Swedes chase us in the group and we're ahead now so they have the work to do."