If you got infinity people on infinity busses, you would only have infinity people, not infinity squared. The moment when you close down the first bus and start with person 1 on bus 2, this person should already be on bus 1, or else must bus 1 be finite.
http://en.wikipedia.org/wiki/Hilbert%27s_paradox_of_the_Gran...
relates one method of numbering passengers on the buses to count them (which I found in another source,
http://faculty.cua.edu/glenn/187f09/hilbert_hotel.pdf
which I used to teach my elementary-age class last Saturday the same trick), which shows that countably infinite buses with countably infinite passengers in each bus can still be accommodated by Hilbert's Hotel, even if all rooms are occupied when the buses arrive.
That's how I imagined the busses to be; two non-overlapping infinite sets. No one from the first bus was also on the second.