I have successfully bonded two pairs in a studio apartment, so I feel your pain about lack of space.

I recommend buying or borrowing an extra x-pen or two, or a pack or two of storage grid cubes (this is prob the most economical option), so you can divide your room in half with fencing, with a buffer between the fences so they can’t access each other. The goal is to have them both be able to exercise at the same time, etc, and not have one penned up while the other is running free teasing them! it is very important that they are not able to nip each other through the bars.

You might even want to restrict both of them to one main room, and then reserve other spaces as neutral and semi-neutral spaces for your bonding sessions. (I used my bathroom as neutral, and my kitchen as semi-neutral, as it was within sight of the main room).

You want your original bun to loose track of what’s “his” turf by swapping cages, etc. And yes, as everyone has said, pre-bonding is very important for them to realize that the other bunny is not a threat (they learn that life goes on with the other bunny around, and they still get food and pets, etc). I personally have noticed a HUGE difference in behavior between my buns between their first speed-date (with no prebonding) and their first real date, after a few weeks of pre-bonding. Everything should hopefully be much more calm after pre-bonding.

Once you complete pre-bonding, stick to the laundry basket sessions for a while (at least a week), since those seemed to be going well. The bath tub seems to upset them, so I wouldn’t use the tub anymore.