Could you explain that one?
If you are pulling on the bars when bunnyhopping you are doing it wrong, end of story. Weight transfer lifts the front not your arms.
The ideal steps to learn are manual > bunny hop > pump > jump
But really in order to jump all you need is to learn how to pump and this:
I would just push into the lip with my legs and that’s it. The rest is a result of physics.
You have already realised you don’t pull with your arms, so its just the push with your legs that’s left. Perhaps body position in the air may help. I tend to squat and pump and the bike comes up under me if I get it right.
You push with your legs and the opposite of what you expect happens. Rather than the bike falling away from you it sticks to your feet. It is counter-intuitive, but it is what works due to kinetic energy.
Think about jumping off the ground as high as possible on your feet. You don’t pull up, you squat down and push. Similar concept on a bike.