With such a central railway station, the train is always a great way to arrive in Bath. Frequent fast trains run from London Paddintgon station westwards (some direct - some stop lots) . Journey time is short - an hour or so but do check prices as London to Bath seems to be a crazy price at some times - try here: www.thetrainline.com or www.nationalrail.co.uk
.... but parking is expensive and the one way system is tedious and not designed for visitors. Parking can be on street (usually limited to 2 hours or in (mostly local council owned) car parks which can be for much longer.
See this link for a map showing car parks closest to Sally Lunns
NEW on the downloads page please see excellent new guide on how to get to Bath.