I have a 150 year old lake house with hardwood floors and a clawfoot tub. I had the floor refinish man put boat shellac on the floor of the bathroom and the screened in porch, that was 15 years ago and no problems ever and all my guests get water on them.

Wood floors were common in every room of the house "back in the day." All you need is a bathmat to step out onto. If you accidentally splash more than that, just wipe it up when you are done. It will be perfectly fine as long as you don't leave the water puddled on it.

Of course, "back in the day" they didn't bath every morning and women generally weren't rushing off to work. Not surprisingly, as people started spending more time in the bathroom and had less time to clean, many opted for lower maintenance flooring.

Ram board is very tough floor protection and is also waterproof. not sure if you can buy just a small roll of ram board, but it could be a solution for you. good luck!

Here is a link that might be useful: ram board tub floor protection