Bush was the 12th player in league history to do it. The last was Eddie Drummond of Detroit against Jacksonville on Nov. 14, 2004.
Both returns came in the second half and were crucial in helping the Saints turn a 20-10 deficit into a 27-20 lead.
Late in the third quarter, Bush's 71-yard return pulled the Saints within 20-17. The game was tied at 20 when Bush ran back another punt 64 yards for a score for his third TD on a punt return this season and fourth in his career.
Bush had a Saints' game record of 176 punt return yards after his second score. His first touchdown made him the Saints' career leader in that category.