The Ditmars/Astoria Blvd/30th Ave area of Astoria has the M60 bus which goes directly to Columbia via the RFK Bridge/Harlem. The timetable says 20 minute trip (which sounds highly improbable given real world conditions). I've heard it can get pretty crowded at times with people heading to/from LaGuardia though. You'd also have the N train there but you would have to take that down to Times Square to pick up the 1 train for Columbia. You can find a good Astoria web community here: www.astorians.com
Astoria's really nice, but I've heard bad things about the local trains (can't speak from experience).
I would advise everyone to never rely on any MTA bus for anything. I live in Maspeth (Queens), which is not very far from Manhattan but also not near to any subways, thus necessitating bus travel for at least part of my daily commute. I can't tell you how many hours of my life I've already lost waiting for a bus. Or being stuck in traffic on a bus because a truck has to back into a garage. Or seeing a bus pull away from the curb just as I reach the stop. And that schedule they put up on the bus stop poles is usually just a cruel joke.
I think what I'm trying to say is, the bus sucks a lot.
Unless the M60 has figured out how to teleport itself, there's no way it's getting from Astoria to Columbia in 20 minutes.