if it's a pre-finished flooring, you have to use whatever the makers recommend as compatible. If bare or sanded wood, I think a floor varnish like Ronseal Diamond would do. Especially as you will often be barefoot so it should not get scratched or damaged like a hall might. It would be difficult to protect the edges unless you treat after cutting and before laying. Any screws used need to be stainless or (fitted with great care) brass.
BTW if you want to colour wood, use a wood dye like Colron, then a colourless stain or varnish. If you use a coloured varnish, the colour will be patchy depending on thickness, and any touching-up will stand out.
Oil finishes are not moistureproof.
Wood does not like getting wet, so you may find it doesn't last well. as Talkinpeace says, the only product sold as suitable for bathrooms is the bamboo which has to go on top of an existing floor.
I have used varnished hardwood 18mm marine ply screwed direct to joists, but it needs a bit of work to stain it into a planked appearance, and varnish. It is somewhat expensive.