What happens if you don't pay your bills?
What If found out so far:
how often does this happen?
It happens per in-game day (48 minutes). You have to pay it, even if you haven't been in your apartment.
You only need to pay, if you are playing GTA Online.
what happens if you can't pay?
You don't lose the apartment and you don't get locked out. What they do - They shut off your water and power, so you can't watch TV, use the radio or shower.
If you can't pay the mechanic, he won't answer your phone when you call him, so he won't bring you a car.