Q: is there a way for someone who is connected to my family sharing to have her purchase be billed to her instead of me? In other words can there be more than one billing method?

If you do not have "Ask to Buy" turned on for that participant, then if they have an iTunes Credit (via iTunes Gift Cards), it will charge to that first. That is the only way to charge them instead of the Organizer's credit card.

Cheers,

GB

Possibly ...

After you set up your family, any time a family member initiates a new purchase it will be billed directly to your account, unless that family member has gift or store credit. First, their store credit will be used to pay the partial or total bill. The remainder will bill to the family organizer's card. As the family organizer, any receipts generated by the transaction will be sent to you. Learn more about how iTunes Store purchases are billed.

Family purchases and payments - Apple Support

If the person has a credit in their account the credit will be used instead of being charged to the primary person, otherwise there is no alternative.  I guess that's how they make sure it really is a family using it where there is a certain level of trust.  Otherwise a "family" might end up being a college dorm.

The other payment control is if one of the people is under 18 at the time of setting up family sharing and ask to buy is activated.

Family purchases and payments - Apple Support - https://support.apple.com/HT201079 - "Are you the family organizer? Learn how purchases work with Family Sharing, what you're responsible for, and how to manage family purchases and payments."

Request and make purchases with Ask to Buy - Apple Support - https://support.apple.com/HT201089 - Ask To Buy can only be turned on for members up to 18.