D.C.
You have a lot of good responses, so I'm only going to add that my 5 yr old, who also hates getting water in his eyes, has suddenly decided that he loves showers. We had to force him in the 1st time (on vacation and there was no tub). But once he realized that he could tip his head way back to rinse his hair, with minimal water in his eyes, he was sold. Now, most days, he refuses a bath and wants a shower instead. You might try it.