I used to live an hour north of Gulfport. Nothing much in the line of traditional shops around that I can remember. There are a few "bow shops" and sporting goods stores that might put you on to a 3-D range where you could get in some practice. The good news is that you'll be right on the coast and the fishing should be great.
Just a few miles north of Gulfport you run into DeSoto National Forest. There are lots of places to hike and explore. I can try to find any regs on carrying a bow outside of season but I don't believe there are any. Gulfport, and all of Mississipi, is very military friendly. You will certainly get a warm welcome and plenty of helpful advice when you get here. I'm sure a few of the trad guys down that way will turn up too. Hope you enjoy your time in the Magnolia state.
Oh, BTW, if you like fresh seafood you'll be in heaven. It is the only thing I miss about being further inland. There's just nothing like getting it fresh from the Gulf! So don't miss out!