The rav does not need to meet you. You do need to get initial information as to whether and how rabbanim in your community accept anonymous questions; if you prefer not to call the rav about this you can probably ask other women in the community, the mikveh attendant, or the rabbi's wife. There will generally be a box or mailbox where you can leave an envelope with the bedikah or underwear, as well as a note including your contact information and any relevant details.
Women do not always try to retrieve the undergarment afterwards when asking anonymously. It may be possible to request that the rav leave it for you in the box where you dropped it off, in an envelope with an assumed name.