Ann's sister, Lauren, is the "L" in "L&M Taxi". They are located at the Lobster Trap by the anchorage. They have Taxi service as well as car rentals.
"We at L & M’s do Taxi & Shuttle Service, Tours, Scooter, Jeep and Truck Rental on the beautiful island of Anegada. You can contact us at 2844410563 or 2844439972"
Also, it's a very short walk (150 yards?) between Cow Wreck and Ann's Tipsy Beach Bar so you can easily try them both.
Lauren is a great option! She's my go-to for taxis if I need them....