The verb-to-noun background of today's phrase was pithily put forward by William Safire a few years ago:

"A similar construction goes from the verb 'to pull aside,' to the diplomatic noun, a pull-aside, which means 'a private meeting at a public event.'" —William Safire, "On Language," The New York Times, August 28, 1994

This citation also serves as the phrase's first appearance in the print media. The earliest reference I could pull aside is from a transcript of some background briefing notes (questions and answers) on "foreign policy issues of interest to the White House":

"Q In addition to the bilateral meeting with Chinese President Jiang in Seattle, is the president going to have bilateral meetings with each and every leader of the members or just some of them?... SR. ADMIN. OFFICIAL: Yeah. I do not think he's going to have bilateral meetings with all of the leaders. ... They are going to take off on Saturday morning and leave most of the rest of us behind and have some time for private, informal consultations. During that time, I am certain he will have the opportunity for what we call 'pull asides' with all of the leaders, a chance to talk with them one on one." —Federal News Service, October 8, 1993