When I taught in Brooklyn, we were lucky enough to be walking distance to the Subway, which the MTA let classes ride for free, if organized in advance. Unfortunately, many of the subways in Brooklyn and the other boroughs are not accessible and not all students were able to participate.
I don't think it is the responsibility of the teacher or the museum to facilitate student travel to museums. Instead, society has a responsibility to offer education to all people and education consists of experiences like museum visits. Is it unfair to expect cultural institutions to foot the bill for education when such visits benefit all people in the society by creating a better world?