Our AMAZING babysitter we have had for two years now makes $10 an hour for our 3 kids. They are 6, 8, and 10, so they are pretty self sufficient.
We use her every week Mon-Fri to get the kids up and on the bus. My husband used to work 2 hours away (and may go back to that shortly) so I have to leave the house at 615 in order to be home to get the kids off the bus. Her normal hours would be 615-815ish (when the bus comes) and she got $20 for that. The kids don't get up until around 7. Lately though, my husband hasn't been leaving until 7 (since he is working 5 minutes away like I do). I am off every other Friday as well...she still gets $20/day - regardless of whether we use her or not and regardless of how long she is there. Even if it is 30 minutes, she gets $20. So I think what we pay her really evens out in the long run.
But honestly, talk to your potential sitter about it. Don't ask what they want, offer something and ask if that is good with them. I'd say $10/hour is fine.