She Took A Bath!! =)
Well, I'm back, and I just thought I'd thank you all for your help and let you know how it went.
On Saturday, I asked Grandma if she wanted to 'take a bath now.' She said she was very tired and to ask her again in a half hour, and 'don't run the bath water until you ask me if I want to.'
So, I gave her the half hour (during which she forgot the conversation), but I went ahead and ran the shower to get some warm humidity in the bathroom, laid out fresh towels, laid out a fresh change of clothes (she's been re-wearing), and used some yummy-smelling soap in the tub water (just hand soap, so the tub wasn't slippery).
I ran the water, went back to her and said, "your bath is ready." She said, "Do I have to?" I said, "well, no, but you're the one who wanted a bath." (That's not totally true, but in retrospect, she DID enjoy her bath, so it's a little true. I don't want to be too manipulative, but at the same time, this was important.)
She agreed and to my surprise, she promptly went to the bathroom and got in the tub. She didn't need any help derobing or getting in the tub (though I kept a close eye while she got in so that she didn't slip.)
I left and gave her privacy, and although I expected her to be in there about 5 minutes, she was in there for closer to twenty. She finally called for me to help her out, which I did. She was exhausted but kept commenting on how nice it felt to take a bath and to be clean all over. She expressed that she just doesn't like the shower very much and prefers the bath, but is afraid of falling. She also doesn't want any help from my uncle, her caregiver, which is understandable, since he is male.
Maybe now, I will be able to convince my mom and uncle to arrange for a female nurse or home healthcare worker to come in once a week and help Grandma with her bath.
I kept the humor going and had her giggling while I helped her. She needed more assistance, since bathing had tired her out. We got her all dressed in clean clothes, and she was good to go.
My entire family was SO impressed with me, and Grandma, too. I wish I was closer, I'd go once a week myself, but that's not possible right now.
Anyhow, we both had a good experience, and I just want to thank all of you for your concern and suggestions.