Adding an electrical outlet to a toilet/tub room
I'm sorry Dave, I'm afraid I can't do that

You can't tie into the bedroom 15A because (a) bathroom receptacles are supposed to be on 20A circuits and (b) bathroom receptacles are supposed to be dedicated to bathrooms. They can either be shared with other bathrooms or with lights in the same bathroom. So the bedroom circuit is not an option.
You can't use the heater circuit unless it is a pretty wimpy heater. Generally speaking, you can't put any receptacles onto a circuit that has 50% hard-wired load. That is not an issue with lighting (especially with LED lighting, but even with incandescent in most residential applications) but it is an issue with heaters. That light/fan/heater circuit is a dedicated 20A circuit because of the power needed by the heater. Typical heaters will use 1500W. Some might be a bit less, but anything more than 1,000W or so and you hit the 50% rule.

What you can do is to add a new 20A circuit (of course) or if there are other receptacles in the bathroom, you can connect to those.

Update based on comments:
It appears that the goal is not to add a &quot;GFCI electrical outlet&quot; per se, which would typically be understood to mean a duplex receptacle for plugging in various devices, but rather the goal is apparently to add another hardwired light fixture. That is a different matter entirely.
An additional low-power lighting fixture, such as an LED fixture designed for use as a night light, can certainly be tied in to the same power source used for the primary heat/light/fan. That solves the &quot;GFCI problem&quot; - no GFCI needed for hardwired lighting. That solves the &quot;connecting to a non-bathroom circuit problem&quot; - that (a) is for receptacles and (b) you wouldn't actually be connecting to a non-bathroom circuit.
There may still be issues with box fill, so expanding the box in some way, or adding another box nearby, may be necessary to make all this work. But you can do it on the existing circuit.
FYI, &quot;you can't put a GFCI on a 15-amp circuit in a bathroom&quot; is not actually true. What is true is that a new bathroom is required to have a 20-amp circuit dedicated to the bathroom (or possibly bathrooms), and that circuit must have GFCI protection for the receptacles. However, if you have an older bathroom with 15-amp circuits (as I do), retrofitting GFCI makes sense for safety - as my electrician did many years ago, I don't think he really asked, I think he just said &quot;you need this&quot; (when he was in my house doing other things I asked for) and he was right.