The train
Great Western Railway runs from London Paddington to Bath Spa. Direct services are often about one hour and fifteen minutes, with some journeys closer to one hour and thirty when they stop more often, including at Chippenham. A few itineraries route you via Bristol Temple Meads and back out — fine if Bristol is also on the trip, a needless reversal if it is not. Check the word direct before you buy the cheapest fare.
Paddington and Bath Spa
Paddington is the Elizabeth line and the Hammersmith & City, which makes it a natural London base if Bath is the point of the weekend: Bayswater, Paddington and even Notting Hill are sane hotels for this particular train. A South Bank hotel means crossing town first.
Bath Spa station is south of the centre, a fifteen-minute walk down to the Abbey and the Roman Baths if the case is on wheels and the hill is kind. The Royal Crescent and the Circus are uphill the other way. Stay near the Abbey if the baths and dinner are the evening. Stay toward the Crescent if the architecture is why you came and you do not mind the slope in the morning.
Other ways
There is no airport in Bath. Bristol Airport is the regional field, then a bus or a train via Bristol. From London that is the long way around. The coach takes about three hours. Driving on the M4 is about two and a half to three hours and ends in a city that is happier without your car in the centre. If you are pairing Bath with the Cotswolds, the car belongs to the villages, not to the Crescent.
The day itself
The Roman Baths are the timed ticket. The Abbey is beside them. The Crescent and the Circus are the walk once the crowds thin. Thermae Bath Spa is the soak if you want the water without the archaeology. Saturdays and school holidays fill the same streets; a Sunday evening after the coaches leave is when the hotel earns the rate.
Compare this journey on Trip.com trains UK rail hub UK rail travel guide