That's not always the case, which I was shocked to find out a few years ago. I live five miles from the county line; in the next county (Eaton, Michigan) all students have access to the public school buses, regardless of what school they attend--so long as the school and the family are in Eaton County.
There is a very strange enclave about forty miles northwest of where I live. Westphalia is a town in Clinton County; Pewamo, five miles a way, is in Ionia County. They have a consolidated school district which includes all of their public schools AND all of their private school (which are Catholic). Transportation is shared, high school sports are consolidated, they even have a shared high school yearbook and graduation. Just little farm communities that figured out how to do what's right for them. Academically, they are the highest achievers in all of mid-Michigan, even surpassing the very wealthy towns like Haslett and Okemos. I don't know how they have escaped the notice of the ACLU, but so far they're under the radar.