Usually, you have a set fee, approximately half your board, and may or may not include half the approx. Costs of shoeing, and maitnance vetting.
But it depends on what the market will bear.
If this is a "little" girl, then maybe twice a week would be better, and she pays a third of the costs. Also, if she is very young, then you must delinieate the rules as to can she or can't she ride without a parent present, alone? Hack out?
You must ride with her a couple of times to see her skill level, including her ability to catch horse, groom, tack up safely and on and on.
YOu must have a contract that protects your liability, and lays out when she would pay vet bills, such as if the horse is injured while she is riding him, especially if there is some negilgence on her part. If it's just a stone bruise, then my feeling is that the owner deals with that becasue their is not negligence involved. Those things just happen sometimes.
Make sure she is a good person to ride your horse in terms of not making him too dull. I mean , taking his training backwards.
Otherwise, don't worry that your horse will like her more than you. That is the LEAST of your concerns.
When you get the right person, you can feel a great sense of satisfaction to share your horse, and knowing that another human loves him as much as you, this is a GOOD thing, not bad.