Simply put, GFIC devices "watch" the white wire (neutral wire)
for excessive voltage. When voltage on return line (white wire) exceeds a preset
level, it trips and turns off the power coming into the GFI on the hot
(black wire) line.
How old is the GFI ? These things can be sensivtive.
Ive seen flourescent lights trip them, and even brand new ones have to be re replaced
because they tripped prematurely.
Also, the present GFI you have in place MAY be working properly, IF you have a
"slight short" in those bath fixtures or wiring.
Good Luck, and please find problem, and dont be tempted to replace GFI with a