My wife and I stayed in a BFVS last Feb/Mar. We had a first floor room, so I can only speak for that. There was a full length curtain that could be pulled closed behind the large doors that opened to the verandah, but no screen to speak of. It did not matter though, as we never had a problem with insects in our room during our entire stay. As a matter of fact, I can't recall being pestered by anything that was flying or crawling during our stay, even on the beach! If you require it, I know that the staff can provide you with citronella candles.
Enjoy your vacation!
We were just there and literally saw one mosquito in a week. Just gotta make sure that you wear bug spray for walks on the beach after dark, because of the sand fleas. You can leave the door to your room open all night and you will be fine. There aren't that many bugs this time of year.
But just remember that you're in the tropics, so an encounter with a bug or two is to be expected....also, if you bring food or fruity drinks to your room, please be sure to get rid of them, as keeping the remnants hanging around will attract those tiny little ants....
That being said, we just got back from an Atrium room with no glass on the windows, and had no problems with bugs.