is she sitting alone yet? if not she is probably sitting with you supporting her? I'd just get a non-slip mat for the tub and put her in with a little water. if you don't feel she can sit, I'd either lean over and support her or get in with her! I wouldn't bother with buying anything for her to sit in, I think at this stage you wouldn't get your money's worth out of it.

If you are worried about the shampoo suds getting on her too much maybe you could minimise it by washing her hair just before you get her out? I've also always just introduced them to having water poured over their heads by doing it a little at a time. If she hates it then just lay her down in the bath to rinse her hair out.

Oh and I forgot we didn't wash hair everyday either, maybe once a week, depending on how much food etc was in it. Just water