Go for a Bonnie
Welcome to the HUBB. Yes, a Bonneville is a great choice for touring, albeit you'll have to kit it out a little whereas other bikes already have screen, luggage, etc.
I took an '04 Bonneville on a three week trip to Scandinavia this summer, all the way to North Cape and back. Did 5,800 miles without any problems. Averaged 50+ mpg, didn't burn any oil, checked the tyres pressures once. The bike has a Scottoiler and it had a full service before I left. Only annoying thing was awful numbing vibration through the bars and the useless NewBonneville rack I bought which couldn't handle bumpy Norwegian roads.
Some owners complain about ride comfort and fiddle with the seat or change the rear shocks but I was fine. There are lots of luggage options, Renntec or Triumph rack and soft panniers is probably the cheapest and easiest. Check the threads on the Triumph tech forum for what others have done. One member is on his way to NZ at the moment on his Bonnie.
Prior to my trip and a long weekend in Germany, I would have baulked at doing more that 150-200 miles on a bike but in Norway, I was regularly doing 300+ miles a day without any problems. Longest day was 422 miles in 14 hours.
Photos of my trip are here if you're interested: Flickr: Triumph trips' Photostream
I also have to agree with flyingdoctor about GS's. Far too many Ewan & Charlie wannabees who seem to think it's the only bike you can trust outside of the M25. The only ones I saw were at North Cape itself and bombing up through Sweden on the Inlandsvagen. I'm sure it's a great bike but for touring on tarmac around Europe, you don't need a big (& expensive) bike with go-anywhere RTW capability.
P.S. The Bonneville was a good ice-breaker with locals who were surprised to see one or who used to have old Triumphs themselves. Fooled a few people who thought it was a '60s - '70s machine too.