bunnies are naturally social, so it might be worth looking into getting another bunny to bond with yours. Then he would always have a friend and it wouldn’t be the end of the world if there were a day here or there where you didn’t get to spend ample amounts of time together.
Charlie is a little like you described sometimes, but usually if I give him time around the house and let him sit with me for a few hours at night he’s fine. If I had the time to bond two together right now I would definitely get him a friend, so if you’re able to have two it might be something worth considering

Most rabbits do love the companionship of their own kind, but there are some who are perfectly happy being the sole rabbit in the house, and they even prefer it that way. It is rare, but sometimes bonds don’t work and the rabbits have to be kept separately, so you would have to make sure that you have enough room in your house for 2 set-ups, if it became necessary.

You didn’t mention if Jasper is neutered or not. Before bringing home another rabbit to bond with him, he will have to be neutered, and you should let at least a month go by after surgery before introducing him to another rabbit. The other rabbit will have to be spayed or neutered too, with the appropriate post surgery time before bonding is attempted. It is generally easier to bond a neutered male with a spayed female, but you can also try to bond same sex rabbits. The BUNNY INFO link at the top of the page has a lot of good info on all the basics of rabbit care, including bonding. Another good article on bonding can be found here:
http://rabbit.org/faq-bonding-multiple-rabbits/

That article mentions waiting 2 weeks after surgery to begin the bonding process, but it’s really better to wait a month or even longer.

You could have a young female in the same room with him, but it would be better for them not to get together physically until she is older and has been spayed and recuperated. At some point, her hormones will kick in and there could be fighting and aggression, then you would have to separate them until after her surgery and some time has passed, then re-bond them. Besides the fact that there could be fighting as she goes into puberty, rabbits can also hold a grudge if they are bitten or somehow attacked. That could make future bonding more difficult.

Most rescues and some shelters/humane societies will have already spayed rabbits – or they spay then when you adopt. Besides saving you money, it will also save you time and trouble. If the rabbit had been previously spayed, after about a week settling in at your home, you could start the bondng process. If she isn’t spayed until you adopt her, you will have to let her recuperate and let a few weeks pass until you can start bonding. In any case, you will need separate cages/pens/set-ups if you bring a new bunny home.