Ok, I'm a cop. I am in Texas, not your state, but the laws are generally similar. You don't have to have a license to ride a bike. You don't have to have ID on you at all times. If you are stopped for whatever and a cop asks you who you are and what you are doing, and you rattle off your name and date of birth, it all jibes (even if you don't have your license on you, if the cop runs you through dispatch and the descriptors match, its good) you are NOT going to have a problem.
The problem comes when someone has no ID, refuses to give his name or date of birth when detained, or gives a name but can't give a birthdate, or gives different spellings for one name, or gives a birthdate but when asked his age comes up with something different. That is fishy. I don't want to issue a citation for some false person or (as is usually the case) the suspect's brother or roommate whose name popped into his head.
I don't carry my ID when I ride my bike. In fact, I seldom even take it with me in the car if I am going to ride the MTB, I don't want to leave it in the car. If I were stopped, I would give my name, date of birth, I know my DL number, and would be surprised if I were even issued a citation for failure to display a DL (different than failure to ID or driving without a DL), although I could be. The cop would run me, find that I match the info given, find that I am without warrants, and let me go after issuing me a citation for whatever he pulled me over for, if he chose to do that.
Having said that, if you are driving the car, take your DL.

