There are several ATMs on Anna Maria Island, including one on the corner of Pine Ave and Tarpon Street, just two blocks down from the Pier. See photo below.
City National Bank - ATM
Located in: Publix Super Market at Holmes Beach
Address: 3900 E Bay Dr, Holmes Beach, FL 34217
Phone: (941) 778-5422
Wells Fargo Bank - ATM
Address: 5327 Gulf Dr, Holmes Beach, FL 34217