Bostic has also been a member of the New England Patriots, Detroit Lions, Indianapolis Colts, Pittsburgh Steelers, Washington Commanders, and New Orleans Saints.

After his father retired from the NFL, he gained his Doctor of Pharmacy degree and eventually relocated his family to Wellington, Florida.

[7] Head coach Marc Trestman named Bostic the backup middle linebacker to begin the regular season, behind D. J.

[9] On October 11, 2013, it was reported that starting middle linebacker D. J. Williams was expected to miss the remainder of the season after tearing his pectoral muscle during the Bears' 26–21 victory against the New York Giants the previous day.

[10] On October 20, 2013, Bostic earned his first career start and recorded eight combined tackles in the Bears' 45–41 loss to the Washington Redskins in Week 7.

In Week 11, he recorded five solo tackles, a pass deflection, and made his first career interception during a 23–20 overtime win against the Baltimore Ravens.

[12] In Week 13, Bostic recorded a season-high ten combined tackles (six solo) and two sacks during a 23–20 overtime loss at the Minnesota Vikings.

[13] He finished his rookie season with a total of 57 combined tackles (45 solo), two sacks, a pass deflection, and an interception in 16 games and nine starts.

[15] Defensive coordinator Mel Tucker named Bostic the backup middle linebacker to begin the regular season, behind D. J.

[14] On December 29, 2014, the Chicago Bears fired head coach Mark Trestman and general manager Phil Emery after they finished with a 5–11 record.

[20] Bostic missed organized team activities due to a back injury, but recovered in time to attend training camp.

Defensive coordinator Vic Fangio held a competition between Bostic, Christian Jones, and Mason Foster for a job as a starting inside linebacker.

[21] Head coach John Fox named Bostic the backup inside linebacker to start the regular season, behind Christian Jones, Shea McClellin, and Mason Foster.

[23] Upon arriving to the New England Patriots, head coach Bill Belichick named Bostic the backup strongside linebacker behind Jamie Collins.

[31] Head coach Chuck Pagano named Bostic the starting inside linebacker to begin the 2017 regular season, along with rookie Antonio Morrison.