From the very beginning, Ms. Bitters seems to already hate Zim, and the feeling is most likely mutual, although there have been cases when she puts her hatred of children aside for the Irken's well being.
One example could be seen in "Dark Harvest", in which she orders Zim to go to the nurse because he had "Head Pigeon" and he actually had the decency to follow that order. This seems to imply that Ms. Bitters is the only person on Earth that he actually respects, similar to his treatment of the Tallest, although it could be because he doesn't want to get expelled by talking back to her in fear of blowing his cover.During the episode "A Room with a Moose", when they were alone in the classroom, she was going to quiz Zim on a copyright information on a textbook. He requested to be allowed to go to the restroom and she did so without a hitch, despite telling him it was his last restroom break for the rest of the skool year. Interestingly, she let him go without the hall pass.
In "Door to Door", she scornfully looked at Zim for making a scene in class and later gave him some tuna as a consolation prize for all the hard work he put into the fundraiser. Whether it was a genuine gesture or an insult added to injury is up to debate.
In "Bolognius Maximus", she politely answered Zim's moose related question, although she was clearly irritated by the stupidity in said question.
Ms. Bitters seems to hate Zim far less than she hates Dib, but unsurprisingly gets equally annoyed with him, which seems to happen far too often, as implied in "Halloween Spectacular of Spooky Doom", where she exasperatedly asked "What is it now, Zim?!" Interestingly, he screams his worries to her, which only fuels her anger.In "Megadoomer", Zim was irritated that he got on Ms. Bitter's grumpy side.
In "Tak: The Hideous New Girl", she hardly cared that Tak caused Zim some harm and actually seemed to ignore his screams of anguish. It can be said that she didn't even try to stop any future assaults in her classroom.
She also doesn't seem to trust Zim much, if at all, since she taped him and showed that he agreed to bring his parents to "Parent Teacher Night" when he denied he did so in the first place; afterwards he asked why she taped that, and when he accidentally hugged her as he was reminiscing on his "cold unfeeling robot arm", she hissed at him.
In "Lice", they were both the only people who didn't get infested by the lice, and when one of the assistants was about to get a sample of skin to find out why they were immune, she frightened him to "take it from the child."
Zim, for his part, does ask Ms. Bitters questions from time to time in order to gain knowledge on Earth's weaknesses for his plans of conquest, but rather than demand them as he would with anyone else, he asks them politely. Most likely this is because of Ms. Bitters' negative disposition and the fact that she is his main source of information about Earth, although it can be said that her lessons are far from accurate and if they are she teaches them in the worst possible light.
In the comic series, their relationship doesn't seem to have changed, since Ms. Bitters still gives the Irken a hard time while Zim just lies to her a lot.
It can be said that because neither of them is human that there is a supernatural connection between them.