You may want to add a photo of your bathroom and the the tile and post your question in the home decorating forum. http://ths.gardenweb.com/forums/decor

You don't need a water resistant rug. No matter what a rug is made of, as long as you let it dry if it's been soaked, it will be fine. But that's the trick: once wet, you need to let it dry. Wool is the best rug material but once wet it takes forever to dry. Synthetics and cottons are your best bet.

For solid colors you can easily find a washable rug (note that sizes larger than 3x4 usually need commercial washers) with a non-slip backing. Despite the mfg assurances, it's better to let the rug air dry than subject it to high-heat dryers; the latex backing will last longer if air dried.

We used washable carpet in our bathrooms for decades with no issues. I still use washable runners in my kitchen. JCPenny has an excellent selection of solid colors but only a few patterns.

Should you prefer a patterned rug, I suggest you get an indoor-outdoor rug that can be garden-hosed outdoors (again, you will be air-drying it). But you will need a rug pad to keep it from sliding on tile.

Indoor/outdoor rugs usually come in a flat-weave, like jute looks. There are some pile outdoor rugs but relatively few; it makes them harder to clean. Here's an Amazon search:

http://smile.amazon.com/s/ref=nb_sb_ss_c_011?url=search-alias%3Dlawngarden&field-keywords=outdoor+rug&sprefix=outdoor+rug%2Caps%2C211

For interior rugs with a good "hand" (e.g., feel) that are easy to clean and Frontgate has a handsome collection of rugs they call EZ Care:

http://www.frontgate.com/indoor-decor/indoor-area-rugs/stain-resistant-total-performance-ez-care/#w=*&af=cat3:rugsdecor_rugs_ezcare cat2:rugsdecor_rugs cat1:rugsdecor

HTH!