This is right off the Government website. Looks like you will be fine as long as you can't easily access the weapon. I can understand using a Bass case if you have one but why not get a proper soft case for your new shottie? I just picked up a two gun softcase for $75.00 and it looks like a guitar case but has the proper straps inside to secure a weapon (2 guns) and magazines as well. It also has two straps on it so it can be worn like a backpack. Anyway, here's the info:
Florida
790.25 Lawful Ownership, Possession, and Use of Firearms and Other Weapons
(5) Possession In Private Conveyance.--Notwithstanding subsection (2), it is lawful and is not a violation of s. 790.01 for a person 18 years of age or older to possess a concealed firearm or other weapon for self-defense or other lawful purpose within the interior of a private conveyance, without a license, if the firearm or other weapon is securely encased or is otherwise not readily accessible for immediate use. Nothing herein contained prohibits the carrying of a legal firearm other than a handgun anywhere in a private conveyance when such firearm is being carried for a lawful use. Nothing herein contained shall be construed to authorize the carrying of a concealed firearm or other weapon on the person. This subsection shall be liberally construed in favor of the lawful use, ownership, and possession of firearms and other weapons, including lawful self-defense as provided in s. 776.012.
790.001 Definitions.--As used in this chapter, except where the context otherwise requires:
(17) "Securely encased" means in a glove compartment, whether or not locked; snapped in a holster; in a gun case, whether or not locked; in a zippered gun case; or in a closed box or container which requires a lid or cover to be opened for access.