Since it is in a bathroom you might want to stay away from MDF, but paint grade poplar, or similar should work fine. You might even rabbet the stock you use to mirror thickness so it will fit tight to both wall and mirror.

Look beyond flat casings to various profiles that have a step (rabbet) in the back. This might be something among chair rail, back band, or wainscot caps at your local millwork supplier (eg see link below). I've even used flooring reducers or transitions. You can see many options if you wander around this site under products/mouldings.

Go to a specialty shop for maximum selection, although the big box stores will have one or two such items.

Karin L

Here is a link that might be useful: Chair rail profiles

You can also simply have any molding pattern you like rabbeted (or do it yourself with a router) and use it.