Acraven has given you good advice for the train from London Paddington Station to Bath. Just one point of potential confusion. Advance tickets, with a capital A, are not just any ticket bought in advance; they are specific discount tickets that are non-refundable, and with them you must take the specific train on the ticket. In return for these restrictions, they're much cheaper than other tickets. They go on sale about 3 months before travel. If you are sure of your plans, they're a great deal; if you're not, don't get them, but get a more flexible ticket. Be sure you understand the rules of any ticket before you buy it.
Now, let me try to help with the London portion.
You won't be using a "rail pass" for London; you'll be using some form of "Tube pass", which will be good for the Underground (tube), DLR, and trains within the London zones you have bought it for, as well as buses within all London zones.
Since you're staying for 6 days, you want a 7 day Travelcard.
London has many zones, but for most visitors, a Travelcard good for zones 1 and 2 is all they need. This is currently £33; each person needs their own Travelcard . The only thing outside these zones that most tourists go to is Heathrow Airport; for that one trip, you can just buy a supplemental ticket. That is, if you're coming in from Heathrow to London using the Tube. If you're coming in from the airport any other way, your Travelcard would not cover the ride - no matter how many zones it is valid for.
A 7 day Travelcard can either be loaded onto an Oyster card, or can be on paper. Furthermore, a paper Travelcard can be obtained from a Tube station (it will have the TFL "circle with a slash through it" logo) or from a train station (it will have the National Rail "crows feet" logo). For transit, there is no difference between the three kinds of Travelcards. HOWEVER, if you get a paper Travelcard from a rail station, it will be good for two for one discounts. Since there are two of you, it might be worth the (slight) extra hassle to get this kind of paper Travelcard. Note that you cannot get a Travelcard that is valid for the two for one discounts at Heathrow. If you're doing this, you have to pay for your ride in from Heathrow some other way, then buy the Travelcard at a rail station in London.
Some details about the two for one deals are here: https://www.tripadvisor.co.uk/Travel-g186338-c133479/London:United-Kingdom:Paper.And.Oyster.Travelcards.2.4.1.Offers.html and here: https://www.tripadvisor.com/Travel-g186338-c195600/London:United-Kingdom:2.4.1.Travelcards.Step.By.Step.html