Inserting bulb into fixture causes circuit breaker to blow,
The GFCI is miswired

It's quite common for GFCIs to be miswired in bathrooms where a light switch is right next to a receptacle.  

I bet if you look at the backside of the GFCI, you will find that the "For Wizards Only" warning tape has been removed from the LOAD terminals,  and a wire has been connected to one of them but not the other.   

I would speculate it is the white wire on LOAD, and the black supply wire loops through the switch and then hops to the GFCI, or vice versa.  

This is typically done when a novice installer has hooked up the GFCI, but has a wire left over.  They see a spare screw behind the "Not For Novices" tape, and go "this is the easiest way to solve my problem, what could go wrong?" In your case they never hooked up a fixture up there, so they were never aware of the problem. 

Since lamp current bypasses the GFCI on one leg, but goes through it on the other leg, currents are unequal and the GFCI trips.  

The answer is to rewire the switch and GFCI relationship so either a) LOAD is not used, or b) whatever is attached to LOAD is wired entirely off LOAD and does not partially bypass it.