i used to live in bath before moving to aus... there is pointings which is nice on lansdown road. jenny's tack shop...although thats more bristol area. cant remember any others right now.
Jenny's Tack shop is really good - its a family run business and the staff are all really helpful. Its sort of between Bristol and Bath - check out their website www.jennystackshop.com.
Wadswick Country Store between Corsham and Bradford on Avon is a huge place that sells pretty well everything! Or Equishop at Wilton, Near Salisbury. Ridemore at Wincanton is also very good if you can get down that way. As you can tell, I am somewhat of an expert on tack shops!