Throughout the series, Mrs. Puff is regularly shown to dislike SpongeBob, often saying he is an "unteachable" student. She continually tries to come up with ways to "get rid of him." This is similar to SpongeBob's relationship with Squidward. Because of his reckless driving, Mrs. Puff gets scared or annoyed when she sees SpongeBob outside of school, like in "Krusty Love" when SpongeBob goes up to her while she is eating in the Krusty Krab, and she panics as if she were doing a driving test with him.
In episodes such as "Boating School" and "No Free Rides," Mrs. Puff seems to give up on teaching or trying to improve SpongeBob. In the latter, Mrs. Puff passes SpongeBob on his test, just to stop having to teach him, even though he did horribly. In the former, instead of disqualifying SpongeBob from the test for cheating, she tries to get him to keep driving successfully so he can pass.
Mrs. Puff's most infamous interaction with SpongeBob is in the episode "Demolition Doofus." In this episode, she tries to get SpongeBob killed by entering him into a demolition derby. Instead of dying, SpongeBob's terrible driving skills allow him to win the derby, making Mrs. Puff more hysterical and depressed than ever to the point where she, herself, tries to kill him.
The most well-known running gag in their relationship is the multiple times SpongeBob got Mrs. Puff arrested by accident. Because of this, Mrs. Puff can sometimes be vengeful towards him.
Despite her distaste for him, Mrs. Puff does attend SpongeBob's parties in "Party Pooper Pants" and "SpongeBob Meets the Strangler." In "The Bully," she stands up for SpongeBob and tells Flats the Flounder not to kick his butt.