The bath tub would probably be safer, but only if you have a hand shower attachment there. That way she couldn't possibly fall.
As far as the blow dryer goes, you can find out how she might handle it while she is dry by holding her and turning it on low warm and holding it near her and letting her check it out first. You'll know if she will freak or not before she's all wet. If she goes nuts over that, you'll know to use warm towels fresh from the dryer! Spoil her rotten!
You could gradually get her used to the dryer probably over time. Most like it because it's warm.