Hi Tim
Went to Iceland a few years ago and had a great time. Didn't travel by bike but did hire a car and saw quite a bit of the country. Take plenty of money as it was never cheap, and after the 'sh*t and fan' coming together over their dodgy financial affairs I doubt if it's any better now. But, on the other hand, if you enjoy Puffin or rotting fish you're in luck!
I know there was a guy from Burton-on-Trent who used to visit this site occasionally who went to both The Faroe Islands and Iceland by bike. He tried to cross through the barran middle of Iceland solo, broke his left and nearly died of hypothermia. He would obviously be a good source of information especially about recovery in the middle of nowhere.
Hope it goes well
Boyd