Luke, if you can find straight trunked fruit trees (good luck with orange trees, they are grown bushy and short for a reason), they'd be worth a shot. I have seen quite a few plum wood bows, but have read that basically any fruit tree will have decent bow wood.
I have seen bows made from pine- not many, and they were very wide limbed, so its possible to make a bow out of non-ideal wood.
Not sure if you are stuck in Tampa Bay city proper, but you should be able to find cedar and juniper trees near you.
The Seminole Indians made bows from Cypress, and it is everywhere near water.
Most of the oaks you will find are red oak wood, some may be white oak, which is very strong.
Out in the bay, you will find mangrove, almost everywhere, even near the downtown area. I know for a fact near 34th street on the water is a big patch of mangrove you could get some branches from (right next to the power plant I used to work at).
I am about 1.5 hrs north of you, and have some ERC staves seasoning, cut in mid September. You are welcome to come grab one if you'd like.
Its funny what Jeff said above about the obsession to cut wood- I never paid much attention to my surroundings when driving, but now- I can't stop scoping out the trees wherever I am, and carry a hatchet and saw in the car now, cause, well, you never know...
Mike