Why did Jess ask Miz Prentice to let him off the bus before his stop?
In Chapter 6, Jess is headed home on the school bus. He's absolutely miserable, because he can't think of a good Christmas present to get for Leslie, and he can't afford anything anyway.
But then, before his stop comes up, he sees a sign that says "Puppies. Free."
How lucky! A puppy would make an amazing gift for Leslie. And he won't even have to pay a cent for it!
That's why he jumps up and asks his bus driver, Miz Prentice, to let him off: so he can go get a free puppy for a Christmas gift for Leslie.
Just as a side note, giving someone a pet as a gift is usually a bad idea. A pet is a responsibility and an ongoing expense, as well as a major decision; it's not a toy. But with that said, the puppy works out as a wonderful gift for Leslie, and Jess feels proud of himself as a result. Let's look at how Leslie receives it:
"[The puppy] was a clever, lively little thing - a present Jess could be proud of.
There was no mistaking the delight in Leslie's eyes. She dropped to her knees on the cold ground, picked the puppy up, and held it close to her face."
If you happened to be reading Chapter 6 quickly, looking for the reason why Jess gets off the bus early, you might think at first that he's going to run an errand for his mother. That's what he tells his bus driver. But we realize he's lying as soon as the narrator tells us in that dialogue tag:
"Lemme off here, Miz Prentice, will you?"
"This ain't your stop."
"Gotta do an errand for my mother," he lied.