GAW,
“I’m trying to figure out what exactly a school district is mandated to supply/pay for private schools”
Just to clarify, the School District do not supply or pay for the schools. The provide these services to all students in a district.
Busing is not a service to the school, it is providing a way for students to get to school.
Special education is provided to students who need it. There are times when the provider most suited to service a specific child is not a public school. There are hundreds of private special education providers in NYC that are not part of the public school system who are paid by NYC Board of Education. Much of them for services that NYC BoE prefers to contract out. These are not costs of the private schools (the schools’ costs) that are paid for by the school board.
I know for a fact that when children are placed in a Jewish special education school in East Ramapo, the amount paid for the students does not pay for any religious studies. The cost for the religious studies part is carved from what is billed. (And the cost is less than the public schools internal cost for providing the services). The religious education program is paid for by the parents and fundraising.
In short, these are mandated services to CHILDREN in the district, regardless of which schools they chose to attend.