How much does this bike cost, please?
or
What's the price of this bike, please?

I presume your question to be, “How much is this bike?” When using “much” the word “money” is assumed.
The “price” is another way of asking the same question, “What is the price of this bike?”
It is not customary to include “how much” and “price” in the same question, since they mean the same.

Cross posted with Teechr

Can we ask "how much is this bike?"

AnonymousCan we ask "how much is this bike?"

Yes, you can, as clearly outlined in wilpeter's answer above.