The match was called off on Sunday following the discovery of a suspect device, which turned out to be a fake bomb left in the stadium by mistake after a terror training exercise.
United have offered a refund to all fans who were in attendance and a free ticket for the rescheduled game and Bournemouth have followed suit by meeting the cost of the 500-mile (805-kilometre) round trip.
"AFC Bournemouth will offer supporters free coach travel to the Cherries' rearranged fixture against Manchester United on Tuesday, May 17," Bournemouth said in a statement.
"Supporters with a valid match ticket will be eligible for free travel."