I would install a clawfoot tub shower curtain (you know, the full circle type). Then, I would duct tape, nail and staple (twice) plastic around the entire enclosure. Showering with a rain coat and rubbers would not be a bad idea either. After each shower I would squeegie, towel dry and then blow dry the entire surrounding area. You know, all of this could have been avoid if you had just installed a drain in the surrounding tile area around the tub.
Still your friend & neighbor.