Like Matt said, we went to St Bart's in July on a St Maarten stop day. We weren't confident with the reliability of the ferries (and it's a good thing because they didn't have one coming back in the afternoon on the day we were there) so we pre booked flights on WinAir out of SXM. Port time was 8-5 (all aboard at 4:30) and our flights were at 9:30 and 2:20 respectively. 15 min flight time.
First things first, you have to be ok with missing the ship and getting yourself to the next port. Start off your day knowing that. Everything went perfect for us until the flight back. The plane didn't show up until 3:20, but at St Bart's there's no screens or anything telling you what is going on. We were sweating.
The taxi to and from SXM is about 20-25 min and will cost you $8-$10 per person depending on how the drivers are feeling.
SXM has all of the typical airport stuff. St Bart's airport is very tiny and just someone checking your passport. Customs coming back into SXM has a decent line. If your docked time is 8-5, I would not do any flight later than 2:30.
I'm a private pilot so I'm used to small planes. I've even flown hot air balloons and gliders. I still thought I was going to die. St Bart's airport is just beyond a decent hill and we basically nose dove in. You can see into and out of the cockpit from the seats.
Depending on the time of year, there may be a separate ship time and local time. If this is the case, you probably can't make it. Google "time in St Maarten". If it's the same time as US eastern time, everything is good to go. If it's different, you run the risk of the captain sticking with ship time and the island being an hour ahead. This really complicates things because you're not quite sure until you're onboard (and can ask- by the way our genie told us one thing and then we had him call up on the bridge and they said another thing)
Also, the shops in St Bart's are only open 10-1 and then they take a siesta until 4.
All of that being said, would I do it again? Yup. It was a ton of fun. Bring your passport and be ok with flying to the next island to meet your ship