Buses run very regularly from Parkway down Gloucester Road - you'll want to get the 73 which takes about 15-20 mins.
From Temple meads it can take around 30-40 mins, especially if traffic is bad. You'll want to get the 72 or 73.
There are a lots of pubs in the area around the ground.
The Wellington is the closest and has a good sized garden and good menu (although rather expensive).
Drapers Arms has seating for about 5 people - so probably not worth consideration.
A little further afield (15 mins from stadium) you have the Inn on the