The agreement is pending league and NBA Players Association approval, standard protocol for changes in a player's contract.
The cost of the bus will be furnished by White.
"They knew when they drafted me there was a fear of flying," White said in an interview with FOX 26 in Hosuton. "That is a very real aspect of my life. There's no reason why it has to keep me from being successful on the court. There's definitely no reason why it should be allowed to keep me from being healthy and I think that that's the main point."
White had not been attending training camp while he and the team discussed the issue.
Specifics about which games White will travel to via bus were unclear, but he hinted at games within the division, such as Dallas, San Antonio and New Orleans.
White has had controversy follow him since he was a prep player in Minneapolis. He was dismissed during his sophomore year at De La Salle High School, one year after winning a state championship. He eventually led Hopkins High School to a state championship his senior year.
A recruit at the University of Minnesota, White was suspended by head coach Tubby Smith for the 2009-10 season after he plead guilty to theft and disorderly conduct for an incident at a Minneapolis area mall. He left Minnesota, and while he had an offer in hand from Kentucky coach John Calipari, his fear of flying was said to prevent him from making the trip to Lexington, Ky.
Instead, he attended Iowa State and led the Cyclones in points, rebounds, assists, steals and blocks. The Rockets selected him with the 16th overall pick.