I doubt insulating one area will make any difference. But if you're doing it, use the XPS as it won't be affected by moisture.

To make a real difference consider converting your vented crawl into an unvented conditioned space.

Here is a link that might be useful: Crawl Space Insulation

I would be doing the XPS under a tile bathroom floor, to make the floor a bit less cold in winter. Tile plus backer plus 3/4" plywood only comes to maybe R=1.5, so an increase to R-10 should make a difference.

Pretty rough crawlspace (rock, rebar) which would need quite a bit of work to make it where plastic could be put on the "dirt". Much of it is well under 24" of clearance, and as it was added on there are 3 separate zones (think of as "peripheral" foundation right through the middle of the house. I also draw combustion air from the crawlspace, so that would need some changes also.

Expect the tile to still be cold, despite insulation. For a small area such as a bathroom, electric radiant heat under tile is terrific.( Unless floor is installed already??).