Bob,
If you've got the room for it, almost anything will work. Bikes have the same problem as any other vehicle as far as noise/interference etc. They can sort of present a problem on the lower bands, they just aren't as 'big' as cars. Certainly doesn't mean you can't do it though, and VHF/UHF shouldn't be any problem.
As far as the headphones/mic thingy goes, it's more a matter of what will fit, both the radio and inside the helmet. The earphone and bone-conduction mic thingy sounds like a good idea to me. No idea about compatibility with any particular radio, so that may only be an 'idea'.
'Course, since you ride a bike, you already know about paying attention to stuff. Adding a two-way radio to that 'stuff' is just a matter of more 'paying' of that attention.
Have fun.
- 'Doc