I don’t know that there is really a particular age that is the best, as every bonding and every bunny is different. I will say that I also have a very skittish shy bunny who improved greatly when he got a girlfriend. He used to be a very nervous bunny, and was so nervous that he wasn’t even very healthy, he wouldn’t eat much, and if my husband left out of town for any reason he would barely eat until my husband got back! Once we got him a girlfriend though he calmed down a lot, and is much healthier now. I think that being in a pair helps them feel that they are not alone, and that there is someone else there to watch out for predators, or other “scary” things.
Is your bun already fixed? That is a very important first step. Once your bunny is fixed, you’ll want to wait another month before starting dating and the bonding process. It is better to do a bonding with a fixed bunny because they are generally calmer around other bunnies and easier to bond, but in addition, two bunnies that are bonded as babies can sometimes have difficulties during their adolescent years as they start to grow into their mature personalities.
Once your bun is fixed (or if your bun is already fixed) – then you’ll want to start taking your bunny on “dates” – introducing him to bunnies to see how he does with them. Often rabbit rescues can help you with this, and what to look for. Do you have any rescues near you?