Bolsonaro announced he would visit Dallas, Texas, instead to speak at an event hosted by the World Affairs Councils of America on May 16.
Separately, Bolsonaro's spokesman said on Thursday that the decision to visit Dallas followed an invitation from Bush.
The far-right Brazilian president canceled plans last week to attend an event in New York City amid pressure from environmentalists, gay rights activists and Mayor Bill de Blasio, who called him a "dangerous man."
Bolsonaro was set to be honored as person of the year by the Brazilian-American Chamber of Commerce at a ceremony in the Museum of Natural History in Manhattan.
Under public pressure, the museum ultimately declined to host the event. As organizers scrambled to find another venue and sponsors pulled out, Bolsonaro scrapped the trip.
De Blasio on Twitter praised the cancellation, saying the world must stand up to Bolsonaro’s assault on gay rights and the environment.