Honestly, central hotels are only a bit more expensive than ones out in the wilds of south London and much more convenient for everything. If you really can’t do the extra money you’re better off on Airbnb.And super close to the British Museum, easily walkable to the National Gallery/Portrait Gallery and on the right tube line for the V&A/Science Museum/NH Museum.
211 bus (see previous on the subject of paying cash) stops outside Victoria Coach Station, and runs to the taxi road at Waterloo. It's a bit of a walk from VCS to Victoria Underground
I will come down overnight by bus...
How long does that take?
You didn't sleep a wink & went home on the train.About ten hours, give or take. Overnight though, so I will sleep most of the way.