Got the train this morning so can give you a up to date reply on that.
Off peak hours (after 9:30am till not sure when) its £3.65 for a cheap day return with a student railcard, before 9:30 its £5.60 (the price without a railcard too). There's usually about 4 trains an hour (not necessarily every 15mins though). Not too sure about the busses, I know the X39 goes to Bristol (search X39 in Bath & NE Somerset on http://www.firstgroup.com/bustravel.php). Prices will probably be on the website too.