When Lee refers to the children as a "delegation" it's meant to be subtle humor or sarcasm in describing the school and the children's social groups as like politics. Delegates or a delegation are usually political terms referring to people who come from the same place or represent the same interests within a political body.
So, if we consider Scout's first-grade class to be that political body, it's made up of different groups of kids from different parts of town, including the ones who live in town and close enough to walk to school and those who are far enough out into the country that they have to ride the bus. When Miss Caroline (who grew up in a different part of the state and doesn't understand local customs) tries to get Walter Cunningham to borrow lunch money from her, the class looks to Scout to explain.
"I turned around and saw most of the town people and the entire bus delegation looking at me. Miss Caroline and I had conferred twice already, and they were looking at me in the innocent assurance that familiarity breeds understanding" (Lee 22).
Here, several factions of children (the town people and the bus delegation) have casually united to appoint Scout as their spokesperson.
Lee is following a pattern that she set up earlier in the chapter by describing the political nature of school. When Scout mentions that Miss Caroline is from North Alabama, she mentions that:
"North Alabama was full of Liquor Interests, Big Mules, steel companies, Republicans, professors, and other persons of no background" (Lee 18).
Describing children as delegates is a way to continue this subtle humor and political metaphor.