I've used the Clayton Hotel in Brum city centre a few times. Normal double rooms do not have baths but on my first visit I booked a suite and it cost me around £100 more but the bath was big enough for 2 and I had a fun in it with an SP on an outcall.
On subsequent visits, I have booked a normal room direct with them and then rang for an upgrade, only 50% success of the 6 times I have done it since but I think my first booking helped. Could be worth a go?