I'm trying to find somewhere to stay in central bath that doesn't have a 2 night min stay at weekends and that doesn't cost a fortune - any ideas?

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Do a search, this is asked regularly.
Most of the chains will do one night - the Holiday Inn Express for example - B&Bs won't: as my mate says, 'Why would I sell one night when I can sell two ?'
The chains are Travelodge (2 hotels - Waterside tends to get better reviews and parking is £5/day) and Holiday Inn Express.
And/or try www.visitbath.co.uk (I think nearly all the B&B's are listed there).
Super cheap: Just up the road from the station is the Bath Backpackers, there is a YMCA (near the central Travelodge) and another called (or it was) St Christophers Inn. If you can cope with a bus ride (and it runs regularly long past midnight) also consider the YHA, in a big old mansion 1/2 way up Bathwick Hill (a useful choice if you need to park a car).
We have stayed at both the Hilton and the waterside travelodge (both for one night).
We are returning to the travelodge and are only paying £35 for one night (room only) car parking is £5/24 hours. It is also a 5 minute walk into town. Tend to get a better breakfast at cafes in town (great one at the bridge coffee shoppe ) than at the travelodge.
How did you get the Travelodge so cheaply? The lowest fare I can find online is 49.50 ;-(
I signed up to the email alert for travelodge and get notified when the sales are on. Sale rooms go "live" at 6am (UK time) on those days.
Rooms in places like bath go quickly.
Travelodge operates a bit like a budget airline/UK train service.
They release quotas of rooms (or seats in the case of transport) at increasing price bands; when the cheap quota is sold out the price goes up a band. These cheaper options are usually non-refundable too.
If you are struggling to find anywhere for your budget, you could also consider staying in Bristol (Temple Meads is about 15-20 minutes away from Bath by train).
If you plan to travel soon you MIGHT find something on laterooms.com or wotif or lastminute.com