A rope bunny is the person being tied in rope bondage. The person doing the tying is a rigger or a rope top. Both terms come out of the shibari and Western bondage scenes, and they describe a role in an activity rather than a personality.
It is not the same as being submissive
This is the useful distinction and the one people get wrong. Plenty of rope bunnies are not submissive at all. They are there for the rope: the pressure, the pattern, the stillness, the way it feels and the way it looks. Rope can be a power exchange, and it can equally be an aesthetic or a sensation that has nothing to do with obedience.
Some rope bunnies are bratty, chatty and entirely in charge of the session. Dom, sub and switch covers the power exchange side, which is a separate question.
What a rope bunny actually does
More than lying there. The person in the rope is monitoring their own hands, feet, breathing and circulation, and reporting what they find. In a well run session they are the main source of information the rigger is working from, which makes it an active role whatever it looks like.
The risk nobody mentions first
Nerve damage, not suffocation. The usual injury in rope is compression of a nerve, most often in the upper arm, and it can happen quickly and without pain at the time. The warning signs are tingling, numbness, weakness or a cold hand.
If any of those appear, the rope comes off immediately. Not at the end of the tie. Recovery is usually weeks, occasionally much longer. Safety shears within reach, every time, and never leave someone tied and alone.
Suspension is a different sport
Floor work is where everyone starts and most people stay. Suspension, taking weight off the ground, multiplies every risk and should be learned in person from someone experienced rather than from a video.
Booking it in London
Rope is a skill, so look for someone who says they do it rather than someone who will try. Sessions run longer than standard bookings because tying well takes time. The shibari guide covers the Japanese tradition and the technique, fetish and domination escorts covers arranging it, and the safe word guide covers the non verbal signals that matter when a gag is involved.