You can’t speed up a bunny bonding. It’s really up to them. If you haven’t bought your new bunny yet I would urge you to take your current bunny to a rescue/shelter for “dating”. It is enormously helpful in getting a pair that will eventually bond. When you start with 2 bunnies that show basic interest or tolerance, it actually does speed up the process. Plus, a shelter bunny is already spayed or neutered, and you MUST have both bunnies fixed for a successful bond. Either one with active hormones because not yet speutered will bring too much aggression to the process.
Take your bunny on some dates, let bunny pick out who they like, and you’re already off to a good start.
Read the INFO section of our site on Bonding for step-by-step instructions on bonding. Also, read-only posts (any older than a month) in the bonding section of the forum will give you insights on how to bond, as well as what can go wrong if you don’t use patience and take care in the beginning stages. Good luck.