I think caging near each other is good, but I'm the one who also says to be a bit cautious. Scarlet is right about making sure the pens are far apart enough that they don't nip. I am always worried that they can hurt each other. I know Rucy got her eye bit, and her bottom lip ripped off by Bailey through the xpen. It was sewn together, but that scared me enough always advise to be careful about putting them "right" next to each other. I prefer to keep an inch or so separate until I can see that they are not being aggressive with each other - supervising their behavior for awhile first.
ALSO, I too have caution on my site in the bonding tips section that if you begin to see them getting territorial with each other and aggressive along the borders then to watch how it progresses. If it doesn't die down over time, ( a couple of weeks) and only increases, then you may need to think of a different route. Each pair really has their own little issues that you have to work through. What's great for one pair, may cause aggression in another. However, they bond bunnies all the time at SaveAbunny so their advise is from tons of experience.
Another tactic is to switch cages everyday. So they get used to the other space, and scent.
Also, ehen they were in the bathroom and they would fight, did they seem to get territorial over a certain space? Like did you have a litterbox there? Sometimes bunnies will get territorial over a box. Also how long is each bonding session right now? Do you end it when they fight or ??
SaveABunny also uses the "strainer" technique that I really like. Use a kitchen strainer to stop a lunge or to separate them before they get into a fight. That way they can still sniff and smell each other though strainer, but they are blocked from full aggression.
Also, be sure you are petting them and keeping them calm. Human interaction to calm can really help, but if you are afraid of getting bit, wear gloves.
And, of course, car rides and those stress methods can really help. I know it's throwing them into a crisis in hopes they'll cling to each other for comfort, and that may seem like a bummer way, but the stress of bonding and not get along is just a ton of mini crisis.
Bonding can really be stressful. On average it takes about three weeks. That means there will be some that are shorter, and some that are longer. It should soon become more apparant what will work for these two. Like switching cages or not, or offering food and affection, litterbox in bonding sessions or not. It can take a few days to figure out what works. And in the meantime, be careful your back doesn't go out from trying to bond them on a small bathroom floor.
Peace to you all! I'm sending easy bonding vibes your way. Keep us updated!
EDITED: I forgot to say - I know you mentioned that your place is small and so not much is "neutral" to your bunny. I know that feeling. When my husband and I lived in the city, our place was small, and our bunnies owned every inch. So we CREATED a neutral place. Check out the bonding section and scroll down to close to the bottom to the BONDING TIPS AND TRICKS and see the first section that says "Don't have a semi permanent Space? Create one: