Bathroom fittings for GU10 bulbs usually have a rubber washer (for want of a better word) in the socket to make the fitting water resistant. This can make the bulb much harder to turn to insert and remove as it grips around the bulb.
I use a gadget like this : Black sucker pad. You can get them on a stick but the hand version (although you have to stand on a chair or steps) is easier. Push the bulb in and out a couple of times to "ease springs" then push in and twist anti clockwise. Sometimes tricky to put bulb back in. My "sucker" came with the downlights. Maybe a local shop would let you have one.