If it is an interior door no problem staining rather than painting - but - since it is a bathroom door it will need a varnish (polyurethane) finish rather than an oil finish. Two easy options;
Stain it to the colour you want then apply 3 clear coats of polyurethane varnish -i.e. wattyl estapol gloss or satin.
Alternatively use an all in one stain and varnish - apply two coats of this plus one clear coat since it is a bathroom door that will get wet.