Revolution (Selamectin) is only prescription-free in Australia, but not if you are in Europe or the USA. In the USA it may be ordered online though without a prescription. It is bunny safe and very effective.
Selamectin is the safest thing, ivermectine works too, but I think you may need a prescription for that too in the USA unless you order online.
I have used permethrin, but it’s not totally uncontroversial as to the safety for use in bunnies. Here is a scientific article that does indicate that it is safe to use permethrin on bunnies: http://www.jarvm.com/articles/Vol4Iss4/Hansen-Beck.pdf I used he smallest little dot of a spot-on-preparation for dogs, right on the spot where the mites seemed to have their centre of operation. It spreads over the skin by itself, so you only need to apply one tiny drop in one place.
Imidaclopride on it’s own is not effective against cheyletiella mites, so Advantage is no good for this.
I would still recommend selamectin though, since that’s what Medirabbit recommends. We are obviously NOT vets here so we can’t tell you what to do, we can only provide info so you can make an educated choice.
Whatever you choose to do, NEVER use any compound containing fipronil (Frontline, EffiPro etc) since it’s deadly toxic to bunnies.
You also need to clean her area + her stuff because the mites can survive without a warm-blooded host for some time. And if you have other pets, they should be treated as well since the mites can live on cats and dogs too, and if you don’t get to the root of the problem, it is likely to return.