I have a shop so I don't have a problem with cleaning space or methods. But, here's a possible solution for you:

While you're at Home Despot, go to the bath tubs and look for "bathtub protectors". When I did some re-modeling, I used them to cover customers' tubs. They are black plastic, cheap, and fit into your tub like a liner. They look kind of like a watering troff for livestock. You can get in there with the bike if you have to. Cut a hole near the drain (no bigger than a quarter) so when you empty it the waste won't smear the whole tub and leave a hard to remove ring. You'll work hard trying to remove that. Cover the hole with electrical tape or duct tape til you're ready to drain it.

Be kind to the salmon - put your oily rags and such into your Homer Bucket.