Ok, so i might just being special, but Bristol Parkway train station is about 15 mins away according to google maps. If i remember my stations correctly, this one would be easier to get to than Temple meads. Or for real ease Yate railway station is apparently 17 mins away. You'd just have to let us know which side of the station you are on.
Hmm, train could be a distinct possibility now too, as Bristol Parkway is on a direct line from Stoke on Trent station. It was the train from Bristol me and BAWRG were stranded on in Birmingham for ages in December as there was no driver to take the train from Birmingham to Manchester...
Living between Temple Meads and Parkway, Parkway is definatly nearest as Temple Meads is nearer the centre of town. I'd imagine a lot of people would have to change at TM, but its only a 5 min journey between the two on the train.
I don't really know about Yate station, but I imagine there are less trains that way.
I use both TM and Parkway quite a bit with travelling home from uni
ETA: there is also a teeny weeny station called Patchway which might be even closer, but having only ever cycled past it I haven't a clue about its usefulness!