Try this.
Dog Friendly Beaches in Tampa, FL, US
I don't know how far away from Tampa your scope is, but there are two places to take your dog swimming around the Bradenton/Anna Maria Island area. One is a causeway between the island and mainland (off leash swimming here), and the other is DeSoto National Memorial Park on the Manatee River (clean, saltwater), where dogs must be leashed but you can have a long line and let them swim. This is on the Bradenton side (mainland). I liked this the best because there is no auto traffic around, as opposed to the causeway.
I also understood that there was off-leash swimming available at one end of one of the Tampa Bay bridges. We haven't been to that, so not sure where it is.