Do you think the load would be hard on an electric timer?

Not if you get the right kind, SRS. I have a number of heaters here*, all on electric timers. Plus, all they are is a clock and a relay, so they're quite hard to overload.

*Some idiot built this place without gas, so I only have electric heating. Oddly enough I tend not to use it, rather put on more clothes. At least one of them is rated for 2000 W, which is alot more thab you'll need for a bathroom, at least in Texas.