IIRC the Germans didn't know HMS Prince of Wales was operational, and believed they were engaging HMS King George V. If anything, they were underestimating the dangers from other Royal Navy fleet units.
The RN wasn't in the best shape right then, especially if they'd just lost Hood and Prince of Wales, though you are correct. Technically, the Prince WASN'T operational, she was on her shakedown cruise, which showed very much. Regardless, disposition of RN Battleships and Battlecruisers in late May 1941, after our little battle:
King George V - Available, near Iceland while this was going on.
Prince of Wales - Sunk
Hood - Sunk
Repulse - Available, but fuel limitations apply. OTL, she had to break off on the 25th to refuel. I suspect after the death of Hood AND PoW, she won't be going anywhere near Bismarck.
Renown - Part of Force H, near Gibraltar.
Nelson - En route from Freetown to Gibraltar
Rodney - Heading to the US for refit, available but fuel limitations apply.
Queen Elizabeth - Mediterranean
Warspite - Mediterranean; Damaged
Barham - Mediterranean
Valiant - Mediterranean; Damaged
Malaya - In the yards, New York
Revenge - Convoy duty, otherwise available. I do not know exactly where she was.
Resolution - In the yards, refitting.
Ramillies - Off Greenland, available
Royal Sovereign - In the yards.
Royal Oak - Sunk
Since in this scenario, Bismarck will be turning around and heading back to Norway, Renown and Nelson aren't coming over play, and Rodney and Repulse will not have the fuel to actually get to her. That leaves potentially King George V and up to 2 R class available. Ramillies will never catch up. Obviously, the Germans don't know all of this. KGV can pursue, but would need to be careful since at some point Bismarck would be getting into the range of land-based aircraft. If Bismarck's machinery remains intact regardless of other damage, KGV is not likely to catch up.