In 1977, researchers from NASA used their experience with the fabrication of space suits to develop a special US$50,000 suit that would allow Vetter to get out of his cocoon and walk in the outside world. The cumbersome suit was connected to his bubble via an eight-foot (2.5 m) long cloth tube so that he could venture outside without risk of contamination.

On the day David, then around age 6, was to receive his gift, many scientists and the press attended to watch the "Bubble Boy" emerge from his bubble. To everyone's disappointment, David refused to wear the suit for the press. A few hours later, after the press had left, he crawled down the tube, but upon pushing his head into the suit he let out a scream and exclaimed, "That's the kind of place where germs live!" He had never taken more than six steps in any direction.

Later he became more comfortable with the suit, but only used it seven times before outgrowing it, never using the replacement suit provided for him by NASA. Both suits were sewn by GE seamstress Alyene Baker. A few years later, when Vetter watched the John Travolta movie based on his life, he laughed when the boy based on him could wear his similar NASA suit right into the bubble without sterilizing it first. David's suit is now on display at the Smithsonian Institution.