I think you should respect the little girl's wishes. She is old enough to have her own concepts of right and wrong, and may feel it to be totally inappropriate for you to bathe her whilst she is naked.
I suggest you don't try to make the girl do anything that she is unwilling to do. If you consider this to be a serious problem, and have the parents' mobile number you could perhaps give them a call and inform them of the difficulty.
On the other hand the girl may be willing to be bathed whilst wearing a swimsuit or underwear, in which case you could perhaps go along with that, and discuss the problem with the girl's parents when they get back.
I am sure you do not wish to trigger a tantrum - that would just make both of you miserable for the remainder of the babysitting period.
-- Best wishes - Majikthise.
I do not know if it is going to work there, but usually I would allow her to get herself wet with clothes on... talking...talking...talking... then has the clothes off...
Just let her take the bath on her own, and when the mom comes home explain to her what the girl wanted to do.
To me she's too old to have someone give her a bath but it should be where u are still watching her
put her in a swimsuit duhhh!