Bath won't work for it really as a) its not deep enough to cover all of your bump and back b) allow you to change position for contractions should you wish/need and c) not good access for MW if need be. You will want to float a bit, kneel on all fours, keep your legs apart etc and a bath is not good for any of that. Chances are your MW won't let you stay in a bath for long periods of time as bathrooms are usually too small for all the people plus equipment etc. Its not a great area for them to work in
Mine didn't like long use of bath in labour once established. Fine in pre labour etc, but it was a birth pool or nothing then tbh.
The pool we bought was great (but not quite ideal if tall like me hence me getting out to deliver) £15 one from Amazon and the sides were strong so able to support me leaning on them etc.
15 mins to pump up the pool, with a large hand pump.
It took about 45mins -1 hour to fill and about the same to empty.
We filled it using the shower, took shower head off, taped on a long piece of hosing and fed it into the pool and left it to run. Then used buckets of hot water to top up also.
To empty there were 2 options for us a) using buckets and b) hose again and then sucking it to get it going to feed out on its own.
Always worth doing a trial run so you know. And having a few pans of hot water to top up.
It really has to be deep enough to cover your bump totally when sat in it. Any less than that and it won't offer enough relief. Same on the back. Needs to be around 37C to actually deliver in so invest in the bath thermometer also
Drop me a PM if you have anything you want to pick my brain over