is it a nut or a bolt that holds the gearbox mount to the car?

It's two 13mm bolts that bolt each side of the mount plate to the car chassis.

There is a big nut and bolt going through the mount attaching the rest of the mount (the bit that bolts to the gearbox).

Only had a quick look as its the gf's car but the end of the mount that attaches to the car chassis seems to only have one 12mm hole in and whats left of the bolt/threaded end that has snapped/sheared/rusted off while she was driving, is still in the car.

So its a nut and bolt with the top i'm guessing comes up in the passengers foot well??

Right,no. Its a box section,you cant get to the nut the other end of the bolt.

You have to remove the mount itself from the body via the two 13mm bolts either side,as Lane said,then bolt the mount to the bracket via the big centre bolt (a new one..),then bolt it all back up to the body via the two 13mm bolts using a jack under the mount to lift it into place.