[3] Bosher played college football at the University of Miami from 2007 to 2010 under head coach Randy Shannon.

In two games in the 2008 season, which were against Charleston Southern and Duke, Bosher attempted and converted all seven extra point tries.

[10][11] He punted a season-high 11 times for 410 total yards in the sixth game of the season against Central Florida.

Against the Virginia in the ninth game of the season, Bosher would tie a career-high seven made extra point attempts.

[15] Against Clemson in the seventh game of the season, he would tie a career high three field goals attempted and made.

[16] He punted a season-high nine times for 387 total yards in the eighth game of the season against Wake Forest.

He punted a season-high ten times for 463 total yards in the fourth game of the season against Clemson.

[22] In his final collegiate game, which was the 2010 Sun Bowl against Notre Dame, he punted four times for 163 yards.

[23] Overall, in the 2010 season, Bosher converted 37-of-40 extra point tries and 13-of-17 field goal attempts to go along with punting 59 times for 2,597 yards for a 44.0 average.

[29] In Week 9, against the Indianapolis Colts at Lucas Oil Stadium, he set a season high for yardage with 321 on seven punts.

[30] On Sunday, December 11, 2011, in Week 14, with averages of 47.8 yards (gross) and 46.0 (net) on six punts against the Carolina Panthers, "ESPN Stats & Information" selected Bosher as the punter of the day in the NFL.

[33] On January 8, 2012, Bosher made his playoff debut in the Falcons' 24–2 loss to the New York Giants in the Wild Card Round.

In Week 13, against their NFC South division rival New Orleans Saints at the Georgia Dome, Bosher had six punts for a season-high 319 yards.

In a home game against the Seattle Seahawks in the Divisional Round, Bosher had two punts for 84 yards in the 30–28 victory.

[38] In a home game against the San Francisco 49ers in the NFC Championship, Bosher had two punts for 90 yards in the 28–24 defeat.

[50] In Week 8, against the Tampa Bay Buccaneers, Bosher did not attempt one punt in the game for the first time in his NFL career.

[58] Against the New England Patriots in Super Bowl LI at NRG Stadium in Houston, Texas, Bosher had six punts for 282 yards in the 34–28 defeat in overtime.

[64] In the Wild Card Round against the Los Angeles Rams, he had five punts for 258 net yards for a 51.60 average in the 26–13 victory.

[65] In the Divisional Round against the eventual Super Bowl LII champion Philadelphia Eagles, he had six punts for 203 net yards for a 33.83 average in the 15–10 loss.