Actually, if the owner won't accommodate you by giving you a way to contact her, you might reconsider going to that salon. That to me is unprofessional especially if you have been a client of theirs for some time. I personally would not recommend going to someone at the salon simply because you were "reassigned" especially if you color or perm your hair.

Perhaps someone else at the salon will know how to reach her like another hair stylist? If you really want to find this stylist, if the salon offers a manicure, make an appointment and get one. Then while there, find out from anyone (other hairstylist, shampooer, manicurist, receptionist) how to reach your stylist.

That said, I still think you will hear from her.