Based on the way he pronounces it (tongue-in-cheek Godfather character accent) it's probably the plural form of the Italian word 'bubbone,' a swollen lymph node characteristic of bubonic plague. It probably developed as slang for an infection because bubonic plague is so infectious. Stewart probably picked it up growing up in the NJ/NY area.
The Daily Show
February 22, 2011
Made famous by Jon Stewart on The Daily Show.
"I can't go out for drinks, I've got the bubons."