If you leave Paddington after 9.30am on a weekday after and buy a flexible Off Peak Return it is £104.70.
If you leave after 10.30am on a weekday or anytime on a weekend a Super Off Peak Return is £75.90.
However there is a cheaper way to Bath, leaving from London Waterloo and changing at Salisbury. Booking Advance tickets on specific trains that is as low as £21 each way, more typically £30 each way. Even leaving London very early .
But you could book that to give a two city itinerary - Bath then Salisbury for evensong at the Cathedral.
That is before any railcard discounts you may be entitled to, say senior (over 60).
If you are going to be doing several day trips from London you could look into a Britrail London Plus pass (which you buy at home before travelling).
If you are going further afield then a Britrail England or UK Pass.
The passes are very good value for money. For instance next week I will have the domestic version of a Britrail UK Pass (a lot more expensive than Britrail). On Monday I am travelling from the Lake District to Penzance with a stop for sightseeing then Evensong at Exeter Cathedral for a per day equivalent cost of £65 first class and haven't purchased anything yet. On Britrail the same journey would effectively cost about £45.
There is also something called the Great West Way Discovery rail pass- £299 for 7 days. As many journeys as you like in a week from London Paddington to Bristol direct via Bath or from Waterloo via Salisbury (from London after 9.20am on weekdays). It includes the Bristol airport to Bath or Bristol buses, many other local bus routes, and all Thames Valley branch lines including Windsor.
That can be purchased on demand.
There is a lower priced East version of the pass (valid as far West as Swindon) which includes the Oxford HoHo bus, and discounts on the Heathrow to Reading and Oxford express buses