Given all the fantastic ideas you've shared with Karen Rani to help Troll Baby get comfortable in the bathtub, it was serenDIPitous (ugh, sorry, I'm a sucker for a pun) that Dave's tip just came up in my queue:
My daughter used to be very timid about the bathtub, it would take a soaked daddy and a crying baby to get her to sit in the tub instead of standing, and she sometimes fell down because she wouldn't sit.
We had previously purchased these little stools to help our daughter get on the potty. They're plastic with rubber feet, so I put one of them in the tub and she climbed right in the tub and was happy to sit on it. After a little bathing and a little coaxing she would get down in the tub and play with the stool and put toys on it and move it around. Now she's gotten comfortable with the bath so we don't need it anymore, but it was a great way to get her to realize that bath time isn't so bad. Although somehow daddy still tends to get soaked.
The stools are really light and small, and she loves to carry them around by the handle and laugh when she shuts off the lightswitch and fan and things. There seem to be a lot of stools like this, but these are the nicest I've found.