After a bit of digging I finally found out who/where they are swimming that weekend (up at the University of Bath swimming pool).
There aren't that many B&B's up there (there is Rainbow Wood farm up there that does them), but students are lazy these days and there is a very regular bus service up and down to the City travelling via Bathwick Hill, the HIgh St and the bus station.
Had you thought about staying in the Youth Hostel 1/2 way down Bathwick Hill?
I suspect that meets the criteria of "cheap and cheerful".
Otherwise there is a block of B&B's on Pulteney Gardens or perhaps the Travelodge Waterside (all an easy walk from the station if you are coming by train).
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