The children through Calpurnia are bridges between the black community and the white community. Because they sit with the black community at Tom Robinson's trial, they are "with" the black community, and have a different vantage point than if they were seated in the "white" section of the courtroom.
Because Atticus Finch has deliberately tried to raise his children without the preconceived notions of racial prejudices, the Finch children are a bridge to the future where black and white are treated as equals in society.
The children represent the crossing-over or a passage from one set of ideas to another. Because of their interactions with Boo Radley, they learned not to judge on surface appearances alone. Because of their relationship with Calpurnia, they learned that black persons are not necessarily evil because they are black.
Scout is a unique bridge as she is outside the social norms for a "girl". Scout is something of a tomboy and is frequently reminded of what it is to be "ladylike", "proper" etc...by teachers and aunts. She is also repremanded by her teacher for reading with her father. Scout is a bridge for women who are smart and ready to be something other than housewives.
Bridges typically touch both sides of an impossible passage. A portion of the children's mindset will be in the "traditions" that they were brought up knowing from their aunts and white relatives. Another portion of their mindset will be firmly planted in the future where truth wins out not prejudice or judgemental attitudes.
There is a song that says, "Children are our future" (Masser and Creed). In that sense, all children are a bridge from the past generation to the future generation. But in To Kill a Mockingbird, this idea has a particular meaning because much of the previous generation in the book retains the hatred and racism that stems back to the Civil War, and actually, before the Civil War. Atticus deliberately raises his children in a way that he hopes will allow them to be a bridge to a new generation in which hatred and racism are no more. The fact that we have elected an African-American president suggests that he, and real people who did the same, had the right idea!