It's definitely nothing to do with bullying, and it's maybe not as strong as hatred. It could also be annoyance, irritation, or frustration.

Sorry, but I've never heard anyone use this idiom in this way; however, I have heard people say: "His music was teeth grindingly bad", which means that his music was so bad that all you could do was sit there and try to endure it." You could also say: "I was so nervous during the test that I started grinding my teeth." Often when people have to do something that they don't want to do, they will also say: "I will just have to grit my teeth and bare it". :) "To bare/show one's teeth" indicates hostility and a readiness to defend oneself. For example: "The enemy forces didn't expect the country they invaded to bare its teeth." Did you mean this one instead?