New GFCI breaker keeps tripping
Mixed Up Neutrals
GFCI does not, despite the name, care about the ground wire. In fact, GFCI can be used in certain circumstances where there is no functioning ground wire in order to improve safety.
GFCI is all about making sure that the amount of current on the hot wire(s) + neutral matches. Anything that doesn't match is current leaking &quot;to ground&quot;, which can be &quot;through a person and deadly.&quot;
Regular circuit breakers do not do anything with neutral. They don't even check to see if there is way too much current on neutral, the way they do for the hot wires. There are all kinds of ways that neutral can be messed up that won't trip a regular circuit breaker but will trip a GFCI.
In addition, older houses often have a lot of stuff on a single circuit - e.g., lights, receptacles, fans, etc. for multiple rooms. Any problem in any part of the circuit can cause a GFCI trip.
Actually, there is one place where &quot;ground&quot; can mess up a GFCI: If a device uses ground instead of neutral (oops, no neutral here, ground &quot;works&quot; so I'll use that instead...) then GFCI is also guaranteed to trip.
The NEC currently requires bathroom receptacles to be on a bathroom-only circuit, but that has not always been the case, and people break the rule anyway. So this becomes a detective job:

Figure out every single device (light, receptacle, fan, etc.) on this circuit.
Open up each box in the circuit and look for neutrals mixed together with other circuit neutrals (e.g., two circuits in one box with all the neutrals together), neutral (white) wires connected to ground (green, bare or a screw into a metal box) or ground wires connected to neutral or other &quot;strange&quot; things.
If you can't find something obvious, start disconnecting things (take pictures and label every wire so you can put everything back together again) and see whether the GFCI problems go away. Once the problems go away, fix that specific problem (post another question here if you need help) and put everything else back together.