If you don't want to know how to get to Columbia, then watch no part of this video, which Irrational Games released just this morning. It's the opening to BioShock Infinite, a mostly cinematic sequence that is plainly an homage to the opening of the original BioShock, which we've included below if you want to refresh your memory.
I didn't catch any "Would you kindly" or obvious ties other than the destination through which Booker travels to Columbia. Its entrance evokes the original lighthouse of BioShock but certainly not as secular in tone.
For those who don't mind seeing how the game begins -- there is essentially zero action here -- have a look, I'm sure we'll uncover more similarities and callbacks to BioShock as this is deconstructed further.