I've broken each collarbone twice. The first one I broke I followed the doc's advice carefully, wore a sling and didn't do any exercise for weeks at the end of which I felt far worse (psychologically) from losing fitness than I did from pain discomfort. With the others I got the same basic medical advice but decided to go back on the trainer within days. I didn't lose much fitness and it had no appreciable affect on how long it took to heal fully --as others have said, about 6 weeks. Funnily enough the only time I hurt (mildly) anymore is when the weather changes--built in baromter FTW!
My advice would be to see a doc as soon as possible after the break to seek if it's bad enough to require surgery (it usually won't be and if it is, get a second opinion because it's is suprisingly not as straightforward a procedure as you might think given the nerves involved and the issues that can result from placing pins or screws in the bone). Get back on the trainer (even if sitting up straight with no hands on the bars) quickly and you'll be able to graduate to riding the bike in a couple of weeks. I found my mountain bike was more comfortable to begin with because of the bar position and the suspension lessening bumps etc.