I also had good results with getting my step-daughter to lay down in the tub to rinse the soap out of her hair when she was that age. It was a little rocky the first few times but -
I didn't fill the tub very deep so that the back of her head would touch the bottom before the water got anywhere near covering her face. Then I would hold on to her (one hand on the back of her head) as she leaned back telling her the whole time I wasn't going to let go (she whined a little the first few times). I think I left my hand under her head at first too but I kept telling her, "this is the bottom of the tub, this is the back of your head, your head can't go back any farther and this is as deep as the water is going to get."
Now she's six, takes showers and does cannon balls into the pool at my in-laws.