"By bike" describes HOW you travelled. "On bikes" describes WHERE you were while you made the journey. Arguably the result is the same, but I recommend using "by bike" as it describes the action and is a little clearer.
To use Blakbatt's example, "They went to the store on bikes" can mean two things:
1) they used bikes for their journey, or
2) there exists a store that sits on bicycles.
ie. who or what was on the bikes??
Common sense tells us to assume the first meaning is correct, but really the whole point of grammar is to save us from guessing in the first place... don't you agree?