Well there are actually two similar postures that mean completely different things. Very subtle
There is a head down, push under the other's nose, with body fully pushed towards the other bunny - That is a dominant posture. Like what Bailey, the white/brown lop is doing to Rucy. Rucy also has her head down, but her butt is higher up, not relaxed, ready to bolt if need be. Plus, what you can't see in the pictures is Bailey pushed into Rucy. Rucy is just responding cautiously before she grooms her.
Then there is a head down, farther away from the other's nose, but again back side slightly up (ready to escape) That is not requesting to be dominant, more of a cautious request to be groomed, more as acceptance. Like how Rucy is in the 3rd picture.
Bailey, the lop, is always pushing - demanding to respected as the top bunny. Where as with Rucy, the gray bunny, she is carefully asking to be accepted. The 3rd picture, Rucy sees Bailey grooming herself, and from a distance asks if she could be groomed too. She is not demanding it, so therefore she is being more passive.
Hopefully that answers your questions. Bunnies really have a subtle language.
Once hierarchy has been established, both bunnies can end up grooming each other as just a display of friendship - Depending on how queenish or kingish the dominant bunnies are.
Also, your bunny may be still mounting him to make sure that even if she grooms him, that he understands she's the boss.