The bathroom in my house keeps tripping. A fan with a built in heater, an overhead light and a few bedroom outlets are installed on the same 15 amp circuit. The thing that gets me is the circuit takes a minute or two of use with the heater on before it trips. It is not grounding as far as I can tell (no continuity from the hot to the neutral or ground). Is the breaker just heating up and then popping after enough current has passed? I'd like two put in two 20 amp circuits, one for the outlet, one for the fan. Can I run 10/3 wire too the bathroom and share the neutral? Is that normal for a circuit breaker to wait a moment before tripping? It also trips when a hair dryer is running.

The heater should have a dedicated circuit @ 20 amps. Anything with heating elements draws a lot of amperage. Hair dryer is another big draw, but if you do what you suggested and separate the heater from the other devices, you should be fine. You can use 12/3 wire and share neutral and ground. I would run 1 circuit to heater only, and the other circuit to the fan, light and outlet. Hope this helps.

Run one circuit to the heat/fan/light unit, and one to the receptacle. This way you do not have two circuits feeding the fan unit.
The heater element itself does NOT need a circuit on it's own. It is likely only 1500 watts tops.

I agree, use #12. No reason at all to use #10.

Every haeter/fan/light I have installed called for a dedicated 20 amp circuit with #12 wire, minimum. The only reason to use #10 is if you have a huge supply with no otheruse for it

Just out of curiosity though, I though that bring housing two circuits in one box (the fan housing) is generally a bad idea?

Just out of curiosity though, i though that bring housing two circuits in one box (the fan housing) is generally a bad idea?
Nope. Not necessarily.