I think this is it:
Ms. Red/Bear was wet from the rain, right? But wait...
Earlier you said
"One sun-shining day in London," so that makes her highly suspect. I'm not yet sure why, but this seems like an important piece of the puzzle.
Another Ah-ha! moment:
The pool-room was literally a room with a pool! The "splash" from "A splash cut the silence in air." was Ms. Red cleaning herself off in the pool, which she claimed was actually rainwater, even though it was _sunny_.
Also,
The maid heard wet footsteps - Ms. Bear rushing back to be the fifth person in the ballroom, I believe.
All of these point to the following solution:
Ms. Red is the killer