How early should I leave for TPA?

Work backwards from the gate, not from the door. For a domestic flight out of Tampa International Airport, most people want to be at the terminal about two hours ahead, and three for anything international. Then add the drive, and then add what Tampa does to a drive at that hour.

That last part is what catches people. The same trip from Water Street, Downtown, Hyde Park can take twenty minutes at ten in the morning and close to an hour at five in the afternoon. Rain doubles it. An event nearby doubles it again.

When you book a car, the concierge sets the pickup from your flight time rather than asking you to guess it, and the car is outside before that time rather than at it. You are not watching an app to see whether anyone accepted.