I've been spending a lot of time researching this for Pinellas County in general.
http://www.stpete.org/Zoning%20Ordinance/Article%2...
A short term rental would not be classified as a "residential use" according to the code. It specifically calls out renting for less than monthly more than 3 times a year.
It would classified as "transient use" which is not allowed in residential
"Residential uses means, for the purpose of these regulations, single-family, child foster home, community residential home, garage apartment, duplex, multifamily, town house, boarding and rooming house, domiciliary and retirement home, and nursing home, which are available for occupancy on no less than a monthly basis, or for less than a monthly basis three or fewer times in any consecutive 365-day period. A use which meets the definition of "transient accommodation use" is not considered a residential use for the purposes of this chapter."
"Transient accommodation uses means a building containing one or more transient accommodation units, one or more of which is occupied by one or more persons, or offered or advertised as being available for such occupancy, when the right of occupancy is for a term less than monthly, such right of occupancy being available more than three (3) times in any consecutive 365-day period. The determination that a property is being used as a transient accommodation use shall be made without regard to the form of ownership of the property or unit, or whether the occupant has a direct or an indirect ownership interest in the property or unit; and without regard to whether the right of occupancy arises from a rental agreement, other agreement, or the payment of consideration. (1) The term includes but is not limited to hotels, motels, recreational vehicle parks, tourist lodging facilities, resort condominiums, resort dwellings, vacation resorts, and dwelling units occupied or available for occupancy on an interval ownership or "time share" basis, when any of the foregoing are made available for occupancy more than three (3) times in any consecutive 365-day period and the right of occupancy is for a term less than monthly."
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You can also call St Pete's Code Enforcement at 727-893-7373 but I imagine they will tell you it is not allowed.
The state law you are referring to is SB 356 http://www.flsenate.gov/Session/Bill/2014/0356/Bil...
The main point being this:
"(b) A local law, ordinance, or regulation may not prohibit vacation rentals, or regulate the duration or frequency of rental of vacation rentals.
This paragraph does not apply to any local law, ordinance, or regulation adopted on or before June 1, 2011."
The code of ordinances from St Pete is already grandfathered in.
It's true there are tons of vacation rentals all over Pinellas County so it is not strictly enforced but if you get a complaint or you start making your neighbors mad you will likely have some issues. Code enforcement is generally complaint driven.
