I think you should ask first, but I bet they'll find that a relief to have you take over the bathing duties.
I ask our sitter to bathe DD, but not DS. It's purely based on age. I get in the tub with DS, because he's 18 months old. DD is 5, and while I stay in the bathroom with her, she pretty much bathes herself and just needs some help washing and rinsing hair. The sitter used to bathe DD and her best friend when we were sharing the sitter. The girls must have been 3 or so.
Until about a month ago, though DS was never in the tub without DH or I IN the tub as well. We can keep a better hold on him that way, and not worry about him slipping under the water. DH is lately comfortable not getting in the tub with him, but holding him from outside the tub. I'm fine with DH doing that, but I don't do it. DS is a little water bug though, and likes to drink the water and stick his face in, which freaks me right out.
I make sure we do a bath once a week on swim days to rinse out chlorine (DD hates the gym showers) and then I aim for 1-2 more baths, but not on any schedule. Just when they look grimy or want to splash. In winter, it's been fine to just do a good hair washing on the swim days and a general rinse on the others.
Last summer I didn't worry about more than 2-3 baths a week either because tiny DS showered with me in the shower sling; if it was often enough for Mama, it'll do for baby IMO. And DD was in the sprinkler daily, which did fine for general rinsing off. We'll see what happens now that it's getting warmer though.
Happy with my DH, 2 kids, dog, fish, and frogs