Riding a Triumph Explorer 1200cc, Bowers set off on his 2143-mile journey to raise money for charities fighting motor neurone disease (MND) after his father Graham was diagnosed with it. At King's College, Cambridge, he met Prof Hawking, the highest-profile person with the incurable disease.
"He was great," enthused Bowers. "I pulled my bike up outside the gate and ten minutes later he turned up with two of his nurses. The street was crowded, everyone was looking and taking photos. We did a photoshot with the guys from MND and when we were finished he took us for a drink. I couldn't believe it.
"There's a pub in the centre of Cambridge called The Eagle. It was a hot day; the place rammed with tourists and students. He just rocked up and they cleared a space in the bar and rearranged the tables for us. It was a lovely half an hour."
Bowers said the journey had restored his faith in humanity. "I've met so many wonderful people, especially the guys who came out to meet me on bikes. They needn't to do it and it's so nice to get that kind of support."
He set off in late June during the hot spell on his nine-day odyssey which took in, amongst other places, Manchester, Glasgow, London, Sheffield, Southampton, Plymouth, Swansea and Belfast.
He said: "The weather was good. The only drenching I got was around Southampton and up to Frome in the south west when the heavens opened, with thunder and lightning."
The rider, who is 52 and has two grown-up children, was invited to visit the Triumph factory in Leicestershire, where he was given a VIP tour by Bruno Tagliaferri, UK sales manager.
"The tour was fabulous. Bruno knew everything you needed to know about Triumph. He had a great rapport with all the boys on the workshop floor. I saw an Explorer being put together. I saw the engine being put into the frame and the lads who were working on it told me a bit about it.
"They don't make batches of models, they make them individually. It's a very slow rolling process but all the parts have to be in the right order at the right time for the right bike with the right VIN numbers. It looked incredibly complex."
Bowers was particularly lucky to get a look around the Hinckley factory as Triumph don't run tours.
"It's all very high tech but unfortunately they wouldn't let me take any pictures. They were very sensitive about that. I think they are quite protective about the processes they use."
Bowers' own bike, which is two years old, had developed a minor intermittent fault at tickover and the factory offered to fix it.
"This guy met me at the factory and said, 'Follow me to bay 10'. I followed him down on this massive, super-clean site and there was a team of three top Explorer techs waiting for my bike and they put in new throttle bodies."
Apart from that his bike, which now has 26,000 miles on the clock, was faultless and handled beautifully. Bowers said: "Getting in and out of central London with the Explorer, a fully-laden bike of that size, was difficult but it was easy at the same time. Riding in London, you've got to be assertive, otherwise you'll get nowhere. You've got to find your spaces and go for it.
"The way it handled the traffic was fabulous, it was like riding a push bike. The only constraint was the width of the panniers. If the handlebars went through then the rest of the bike did. By the time I got out the other side of London, after three or four hours I was goosed. I was cooking in my leathers. I've much respect for the bikers around London. I'm surprised they've got a lifespan of more than year."
The Irish leg was another highlight. He said: "Three Irish bikers met me off the boat at Dublin port and they rode up to Belfast with me. The welcome of the Irish was fantastic. They were really glad that I'd made the effort to go over to Northern Ireland.
"We bumped into a hen party on the way to Belfast. There were seven or eight of these women, who were old enough to know better, in bright, lurid polka-dot dresses. We got the bride on the bike for some photographs and they all gave me a load of money towards the charity. It was a great, spontaneous hoot."
Bowers, from Manchester, will split the £4400 he has raised so far between the MND Association, in England, Wales and Northern Ireland, and MND Scotland, as he had Scottish grandparents. He visited the charity's Glasgow office last month to meet the staff and volunteers on his trip.
He said: "My dad's been massively appreciative of it. He's been blown away by the generosity."
If you'd like to donate see www.justgiving.com/teams/mnd-gb-motorcycle-tour
SKILLS FOR LIFE
I'm officially an advanced rider after passing the Institute of Advanced Motorists' Skill For Life test last week, thanks to the endless patience of the Glasgow South group. The course costs £139 and has made me swifter, smoother and, hopefully, safer. Following the demise of Bikesafe in Scotland, which Police Scotland don't run, the IAM are offering riders in Scotland a free assessed ride to sharpen up their skills. You don't need to sign up to the IAM, or any of their courses to take part. See www.iam.org.uk. Go on, you know it makes sense.