How does one (if one does) apply the first amendment to each thing subsidized by tax dollars? If the government is involved in it, is religion automatically out?
To answer the second question first: no. In fact, if the government discriminates against religious viewpoints, it usually falls afoul of the Free Exercise Clause. (It may also violate the Free Speech clause, as the government generally isn't allowed to discriminate between speech that expresses a viewpoint the government likes and speech it doesn't.)
For example, if a public school allows all other student groups to use school facilities, but refuses to give the Christian students association or other religious group the same privileges (with the same conditions), that's probably a Free Exercise violation. That would be true even if all religious groups (and/or atheist groups) were denied access. I vaguely recall some cases like this, but I'm too lazy to look them up at the moment.
The problem with school prayer is really the indoctrination/forced speech/peer pressure aspect of it. The government is putting its imprimature on a particular prayer, and there's almost no way to do that without favoring religion generally, and likely one religion or group of religions in particular. (Ever seen those joke "inclusive" prayers that supposedly mock political correctness? What they really show is the impossibility of having a "neutral" prayer that is at all coherent.)
We had another thread here not long ago where we discussed the fact that a true comparative religion class, that studied religion in an impartial, non-proselytizing, and academic way, would be perfectly constitutional. The problem is that there isn't a huge demand for that kind of course in high school, so most religion classes that are likely to be offered are probably being done for proselytizing purposes.
Anyway, in the context of bus advertising, once the government decides that it's going to accept paid advertising, then it is very limited in its ability to reject particular ads. We've seen this before in the context of "sponsor a highway" programs, where the government lets community groups or businesses put a sign on a highway in exchange for a donation. The government can't decide that it's ok to allow the Loyal Order of Waterbuffaloes to sponsor a highway but not the KKK.
Edited to add: I don't want to make it seem like there are a lot of clear answers here. Religion clause jurisprudence is incredible complicated and full of contradictions and nuances. It's one of the rare situations in constitutional law where the government can't really err on the side of caution, because there is no safe side on which to err. The government has to navigate between the Scylla of the Free Exercise Clause and the Charybdis of the Establishment Clause. That's a course that even nine Supreme Court justices can't agree on always, so it's hard to expect even well-intentioned minor government officials to get it "right" all the time.