Bairstow who was dropped from the Test squad for the two-match series in New Zealand, made the cut in the Kiwis Twenty20 squad for the tour that begins in November.
Eoin Morgan, who led England to their maiden World Cup triumph with a win over New Zealand in July's final, will return to take up the captaincy for the T20 matches as they step up their preparations for the World Cup in October next year.
"It's going to come around thick and fast. Seeing guys who've played county cricket taking the step up to international cricket is going to be fascinating. That, coupled with the guys that are not on this tour but will come back into the team, there's going to be competition for places."
England won their maiden 50-over World Cup title in July this year, after a thrilling final against New Zealand at Lord's, and Bairstow hoped that his side's 50-over success could spur them on to T20 World Cup glory next year in Australia.
"The cycle for the 50-over World Cup started four years ago," he said. "Hopefully, we're fortunate enough that the way we've played our 50-over cricket will lead us well into our T20 cricket.