Just so happens we stayed at Bahia Honda the middle of April 1999. We'd been at Long Key State Park for two weeks and had to leave because of time limits.
We were just winging it in those days, so we arrived at Bahia Honda with no reservations and got like the last available campsite. We left the next day... the mosquitoes drove us out! We were not near the water, and there was very little breeze. We headed back to Long Key and stayed there until May.
Forewarned is forearmed... long sleeves and long pants and plenty of deet.
We also stayed at Jonathan Dickinson State Park in 2001, about the same time of the year. There is actually two separate campgrounds, one close to the highway, the other way back in. If you want quiet nights, ask for the farther campground. It really is a very pretty park. If you ride your bikes around, stop and look in the culverts for the baby alligators!
It's about 80 miles from Homestead to Bahia Honda. If you're driving during the daylight hours, you can pretty much count on doing the speed limit or less from Key Largo south.
After you get setup and decide to go to Key West, you be sure and stop at the Sand Bar Restaurant for the best grouper sandwich and a cool one. It's on the right hand side of the road, somewhere near Little Torch Key. You can't miss it.