It's a quick bike ride trhough the Gulf State Park which connects to Sun Outdoors. Even faster if the bike is electric. Sun Outdoors had regular bikes and electric bikes for rent and Gulf State Park has many miles of trails, including beach access and a bridge to get you over the highway without stopping.
It is a 12 to 15 minute drive to the beach. You can walk from the resort through the state park and directly to the beach. It would be a pleasant walk, but also about 4 miles each way.