Anyone who has Admin or Editor status of your artist's Facebook page can access your artist's Bandsintown page in Bandsintown if they login with their personal Facebook account login information. To add an admin, click “Settings” in the top-right corner of your artist's Facebook page, then click “Page Roles” on the left and add the person you want to manage your page as an Admin or Editor.
They can also sign up on Bandsintown and apply for verification to manage the artist by following the steps here!