Didn't you just answer your own question. You take a bus to south beach, that's a beach close by. Biscayne Bay and Key Biscayne are one in the same. By the way, they're not close to Daytona Beach, St. Augustine or Jacksonville. It is real close to Miami and South Beach.
Is Key Biscayne close by? Is this a better area. Is there a nice beach there? Good Hotels?
Key Biscayne is a barrier island in Biscayne Bay - southeast of your favorite hotel. It is mostly state parks - with Crandon Park on the north end and Bill Baggs State Park on the south end. The middle part of the key is some exclusive property and there are hotels - most notably a Ritz-Carlton. As Penny notes - you are almost there. There is a causeway that goes out to Key Biscayne. I spent a lot of my time at the beach at Crandon Park in the 1960's, when we lived in Coral Gables.