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 Green - which is a very good pub, small garden.
Also highly recommend the Royal Oak and Lazy Dog both within 15 mins of the stadium.
Avoid the Duke of York and Queen Vic!
If you are coming from Temple Meads or the town centre the walk up Cheltenham Road and Gloucester Road is nice (about an hour) - and a very good pub crawl!