The way I see it, you have a few options. They might or might not work for you, but just throwing them out there…
1) Will the rescue do the “heavy” bonding work and return them to you “pre-bonded” so you can just finish it up? This would require giving them both up for about 2 weeks.
2) Can you keep them both separate for awhile longer? Wait until you’re feeling better? There are bonding exercises you can do without the buns ever meeting face to face. You can exchange litterboxes or bunnies each day to switch up the scent in their habitats, or you can give each a bunny “stunt double” that smells like the other.
3) If you move ahead with bonding now, do you have a buddy who could help? Even if they’re not a rabbit person, there are great articles about bonding and bunny body language that they could read, and then you could go through this with some “back-up”.
I have a similar reaction with new pets. For the first week, it’s the biggest mistake ever… but it gets better as I get more attached. Maybe that’s the 4th option. Try and develop a relationship with the new bunny before bonding. Once you’re bonded to them both, you’ll be more determined to make it work.
Bonding should be done everyday for quickest results, but do what you can do. If you can only do every other day, or a couple times a week, no one is going to judge your commitment.