First off, I think you guys look great together and your horse looks wonderful, I would never guess he is so old. [:
There are a couple things you need to fix, just like everyone else though. I realize the pictures and video were from a few months ago, but I would be willing to bet that you still have the same position problems. The biggest thing I see is your release. In the video, you look like you're bracing yourself on his withers for balance. I can understand how jumping bareback would induce that. You need to pick your hands up and then give him a good solid crest release. Grab mane, jumping bareback makes it easy to accidentally pull on your horse's mouth and grabbing mane would ensure that he doesn't get a jab in the mouth for obeying you.
You also need to have a much better approach. Trot around the arena, find a nice trot or canter, get into a rhythm and give him a decent approach. Count your strides as you come up to the fence, it will help you begin to see distances easier and will help HIM learn to see them.
Your bum does not need to lift off of him at all when you jump him bareback. Just let him close your angles when he lifts off the ground and give a good release. The way you are jumping now, you are ahead of his center of gravity and making it harder for him to lift his legs and clear the fence. He's a bit older, help him out by staying back.
Your leg looks good, but I would do a lot of no stirrup work WITH A SADDLE to strengthen up your calf and thighs. Posting with a saddle develops a completely different muscle than riding bareback does. You don't have to jump him with a saddle, but you DO need to practice flatwork with it.
Overall, you guys look very good together and your horse is a cutie. Good luck with his jumping!