Why does a dog excesively groveling until being bit?

It is possible that your dog is doing this as a way to belong with the other dog because of feeling unsecure. Most of the times he just needs to feels that "you have his back". Once he has that connection with you while around other dogs he wont need their approval as much.

There are many ways to get him to understand that you don't like a behavior, some dogs do just fine with just a voice command. Another techniques is to use treats/toys, but you should factor in the reaction of the other dogs then using treats/toys as they might react too strongly.

If you decide to use a command to help with this problem find something that works for you -even if it seems silly or doesn't make sense to anyone else. I used "keep moving" for one of my dogs that used to freeze up a lot when approached by strong minded dogs. While teaching a new command always follow immediately with an action that makes your dog do what is asked of him.

Dogs learn from repetition, so any time you successfully get your dog to do the right thing he is more likely to do good/better next time when in the same situation. And any time you allow him to do an unwanted behavior he is more likely to repeat that as well.

Whenever he is doing that action try to have a high valued treat such as chicken, hotdog, cheese, etc. and lure him away from doing the groveling so that he associates that whenever he licks he is not supposed. Even if you catch just about to lick another dog put the treat right in front of his face so that he learns that he's not supposed to lick other dogs excessively.

Sounds like your pup has confidence issues. Work on training him in general. When he meets new dogs, let them be on other side of gate etc and put him through his paces. Sit. Down. Shake. Up. Down. Spin. Sit. Etc. This can help take his mind off of trying to submit to new dog and instead focus on you.

Another easy thing to do is before they meet, take him for a run. Not a walk. A run. Get him super exhausted. Then when he meets dog and tries to do his kissy face routine, you can tell him "leave it" etc and he'll be too tired to put up too big of a resistance. Obviously he should already know the leave it command or something similar. After all if he starts licking your ice cream, you'd tell him to stop. Apply whatever principle you use in that situation.

Think how would you feel if some guy would kneel and snatch up your hand kissing it as if you're royalty. You chuckle and say, alright dude that's enough. But he won't let go off your hand, just keeps kissing, slobbering, licking and bowing over it? Annoying right? The other dogs know that that behavior is obsessive and are "disciplining" him. They might be getting overly frustrated because you're the adult so to speak and should be stopping the behavior. Go ahead and step in and be Daddy! :D