Sounds like a big job, :-)
I minimize the area affected by bathing in the kitchen sink with towels around within shaking distance. Immediately I am done, I put a towel around him so no more mess .
I can imagine areas around the bath are difficult and hope you can either do it in the sink or by other technique that others here may suggest. Good Luck
By the way I don't seem to have a hair problem, perhaps a brush down before the bath to catch the loose hairs?