Waterproofing 1st floor bathroom with original wooden floor boards in a Victorian house
You could sand down the floors, and refinish them with oil based stain and polyurethane. That should be enough protection to keep the floors from rotting. You could do what they did in the old days and put towels down around the tub and wipe up spills immediately. Standing water will leak through the cracks between the floorboards.

You could also good clear polyurethane caulk meant for bathrooms and fill the gaps between the boards around the wet areas, or on the entire floor. This should prevent water from seeping to the room below.