First, you want to have him associate you with pleasurable handling. Picking up a rabbit is not their favorite thing, and he sounds like my Samantha, who won’t let me pick her up at all. But she comes to me on her own for face rubs and pets. You want to be on the floor with him, let him get curious about you, and pet him gently around the face and ears to get used to your touch regularly.
As for picking him up to catch him, I found that she could be trained to a routine of coming on her own with a treat reward. I shake the treat bottle each morning and place one inside her food dish in her cage, and she comes running for it. She now goes into her cage at the right time and looks at me until I get her treat in there with her. It’s the basis for clicker training, which is a total reward for good behavior system.
That’s my next suggestion. You can read up on clicker training and start now, so in case of an emergency you can have your bunny already trained. That said, I know it’s very hard and takes a while.
So you want to catch a bunny quickly by throwing a light towel over him and scoop him up and into your chest while wrapped in the towel. If you can get him where you need him, then set him down gently and only then unwrap the towel so he can see that he’s on the ground again, he should be mad but fine. Get the door shut quickly at that point so he doesn’t escape. I learned that the height was scary to my bunny, so she does better with her eyes covered if she needs to be lifted at all. Some bunnies don’t need a towel if you can scoop quickly and firmly into the crook of your elbow while carrying him pressed to your chest.
Herding is another way to get your bunny where you want him. You pretty much stand opposite the way you want him to travel and move toward him so he moves away from you to where you are trying to get him. If you can herd him into a room, or an increasingly smaller space, you can block his escape with a baby gate, closing a door, or eventually caging him.