Answer: There are two separate issues here. One is whether the student should be transported to school. The answer to that is yes. The district has placed the student in this program, and transportation is a barrier to her enrollment and retention in the program. Therefore, some transportation assistance must be provided. This is a district placement (via contract notwithstanding), so transportation needs to be arranged/provided if it is a barrier. It is unclear whether this is a special education placement, but if it is, the Individuals with Disabilities Education Act also would apply.
The second and separate issue is who pays. The McKinney-Vento Act would not dictate who pays in this situation. It appears as if this is a question for the district and the program to jointly resolve. It depends on the MOU or contract between the district and the program, their practice, etc. The bottom line is that this a district student, so, ultimately, the district has the legal responsibility to address barriers. However, we can’t really opine about whether the program should provide or pay for transportation. This is probably a question for the school district’s special education department and/or other administrators.