painting the bathroom
Is the tile ceramic? There are products on the market that you can use to paint ceramic tile (tubs, sinks, etc) that are made to get wet. You'll have to first coat your existing tile with an undercoat (primer) specifically for the surface (and probably sand a little before putting it on), then paint with the ceramic paint after the primer dries. There is also protective finish that you put on after the paint.
I don't know the exact name of the products I'm talking about, but Home Depot sells it...as I'm sure most hardware stores do. I haven't used it myself, but I've read about them in HGTV's website as well as other home improvement sites.