Hi there! Welcome!
Don’t despair! I think one of the most common mis-conceptions about bonding is how long each step in the process takes. You did great by having them live side-by-side, but the process of having them get to know each other in neutral territory takes a bit of time, even in easy bonds. It’s also really great they do not fight in the car.
To start, the bonding area should be basically empty at first. Tunnels, litter boxes, etc. can all cause more disputes. Pick an area that neither rabbit has been, and ideally not in smelling-range of the area they currently live. Bathrooms are commonly used for this because most rabbits don’t go in them and they are easy to clean. 🙂
Each day you will put the rabbits together in the neutral spot (let’s say the bathroom for example) and supervise them very closely for a short period of time. I find it helps to set short time goals. Since your buns did OK for 10 min already, I would try for 5 minutes. Be right there with them with leather gloves on (or oven mits LOL) so you can intervene if needed. Your goal is to prevent fights from occurring, rather than breaking them up once they already start. I like to do a lot of petting in early sessions. When the buns approach each other and come nose to nose, pet them both a lot and swap scents. This makes the buns think the other is grooming them and keeps everyone calm. End the session on a good note (even if they are ignoring each other). If the buns fight right away in the session, you can start and/or end the session with a car ride together.
If 5 min goes well, the next day go for 10. Then start bumping up the amount of time they spend together as long as they aren’t fighting more at the end of the session than the beginning. Usually when I get to about 20 min I like to start increasing the session length more (like I’ll go for an hour, then 2 hours, then 4, etc.). If the sessions get worse towards the end, then do shorter sessions and possibly switch up your bonding area (different area, or make it larger or smaller). When sessions get long (6+ hours) I usually try to add a new litter box, but if it causes disputes I remove it. I put pee pads on the ground to make clean up easier (and keep them from just standing in pee!).
Once they can spend several hours together without fighting (a little nipping is OK but nothing major), then you can try some really long sessions or an overnight (prepare not to sleep much!), or you can opt to “marathon” bond. Basically your goal is to get to 48 hours with NO fighting and lots of positive behaviors (grooming each other, cuddling, sharing food, litter box, etc). After that you can transition them to either a semi-neutral space (usually within site of their main home but not in it) and supervise another 24 hrs, or you can go straight to the final home. I often haven’t had a great semi-neutral spot so I typically like to spend an extra day or two in the neutral spot. The nice thing is after the 48 hrs in neutral you don’t have to supervise them in that space as closely, so I usually use that time to get some sleep and get their new home all cleaned and ready for them.
After they move to their final home you supervise for another 48 hours and if that goes well then they are bonded!
Not everyone has this kind of time to supervise constantly, so it’s OK if you need to separate them for periods of time when you can’t watch them. The key (IMO) is for them to spend several overnights together without issues, because fighting tends to happen overnight or in the pre-dawn hours when they are most active.
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.