Agreed! Teachers have to jump through so many hoops to book field trips and buses are extremely expensive -- this is compounded when teachers only have the leeway to have a field trip on a single day, and thus must bring more students, and thus must order more buses...
NMAJH also has a bus (and admission) scholarship for all Title I schools and other groups demonstrating financial need. I don't think every single museum does this, of course, but in my experience it's a common enough opportunity, at least among larger museums.
Fortunately, at least for us, subvention funds is the single easiest category to fundraise for, to the point where this fiscal year we actually have more funds than we'll likely need (but that we can't use for other purposes). Donors love helping students!
I think it would be interesting to explore the other ways that museums and other historical institutions can support teachers along this vein. What if, for example, a museum were to help facilitate the sponsorship of a class or grade, helping donors to buy textbooks, pencils, and other supplies for teachers? I'm not sure how this would work, especially if there were no other connection to the museum, and I can definitely see development staff worrying about "losing" the donor to the school... But definitely something to explore further! Or, especially going off of @engledd's idea, if we pooled all those scholarships to create like a centralized bus/admission scholarship in each geographic area, which would also help out smaller museums that don't have these funds or resources...