How do I market myself to a client who is seeking a more experienced bookkeeper?

Be honest. One of the mistakes new freelance bookkeepers often make in a hurry to sign up new clients is to accept anyone with a wallet. That is a mistake. In the beginning it is important to establish the reputation as a high-quality bookkeeper. This is how you plant the seeds to receive client referrals. Clients hire us as professionals and expect us to lead them. Not the other way around. Therefore, only accept clients who have uncomplicated bookkeeping needs in the beginning, or who are in and industry that you understand well. If you need experience it is better to provide quality services than to get in over your head, cause a mess of the books and get a bad reputation. If a client wants a more experienced bookkeeper, be of service and help them find a qualified colleague. You’ll get a good reputation with a possible peer referral source, and who may be willing to refer potential clients with less complicated bookkeeping needs to you.