Bush gained 23 rushing yards on nine carries and added 11 receptions for 63 receiving yards.
His touchdown came with 4:18 left in the game and capped the scoring.
Drew Brees completed 21-of-33 passes for 171 yards, one touchdown, and no interceptions. Deuce McAllister rushed for a touchdown on 15 carries for 123 yards and Joe Horn made four receptions for 48 yards for the Saints (4-1), who bounced back from their only loss of the year, 21-18, last Sunday at Carolina.
Bruce Gradkowski, starting for the injured Chris Simms, went 20-of-31 for 225 yards and two touchdowns. Joey Galloway caught four passes for one touchdown and 110 yards while Carnell "Cadillac" Williams rushed for 111 yards on 20 attempts for the Buccaneers (0-4).