For jumping bareback, like the person above said, don't allow your lower leg to swing back. This will cause you to fall forward and lean on the horse's neck, both making it harder for the horse to jump and making your seat a lot less secure.
Stretch your legs down long when you are bareback, as this will make you more secure, and make sure you keep your seat through balance, and not grip. Without a saddle horses are usually a lot more sensitive and if you grip, the horse might think you're asking it to go forward. Also, gripping makes it harder to keep your balance.
Keep your heels firmly down all the time, this is the key to preventing your leg from swinging back and keeping a good position.
Maybe you could practice jumping without stirrups a bit before trying bareback, if you haven't already? That would be the best way to prepare, because it's basiclly the same thing only bareback, obviously, is slightly more difficult.
Anyway, good luck, jumping bareback is a lot of fun when you get the hang of it :)
There are only two emotions that belong in the saddle; one is a sense of humour and the other is patience.
- John Lyons