What's the wattage of the heater? A lot of 120V heaters are 1500 watts which means they'll be drawing 12.5 amps max. If you have a dedicated circuit I don't think it would probably be a problem putting a 15 amp breaker on it. There's some chance the breaker would pop due to inrush current or something, but I doubt it. That's not to say it will be up to code. I don't know anything about code, but I bet it would work.
This is exactly the situation I currently have in two of my bathrooms. The two I haven't redone yet. They have 15 amp breakers on the outlets, and they also feed the lights. My freaking kids turn on a space heater (I'm putting radiant heat in all the bathroom floors eventually), then turn on the lights. Periodically this practice blows the breaker. But if the lights are on, and you turn on the space heater, it's typically no issue whatsoever.