BB is on the record as saying he doesn't like to use inexperienced players at positions that involve a lot of on-field decision making. He is also on record as explaining that the closer to the center of the field you line up, the more on-field decision making is required - especially behind the front lines. Thus, the QB position on offense and the middle linebackers and safeties on defense do the most on-field decision making. This is his own explanation for why he doesn't generally use high draft picks on these positions.
If you look at the starting linebackers in the BB era, we have:
Tedy Bruschi - low round pick, played DE in college, had 6-7 years experience before he became a starter
Mike Vrabel - mid-range free agent pickup, experience in 3-4
Rosy Colvin - high-price free agent pickup, pass rushing specialist who had demonstrated high success in the NFL.
Willie McGinest - very high draft pick (#4 overall) inherited from previous regimes, played down lineman before transitioning to linebacker, several years experience before BB got him.
Ted Johnson - high draft pick, inherited from previous regimes, several years experience before BB got him.
Roman Phifer - very experienced veteran free agent pickup who played for BB for the Jets.
Bryan Cox - see Phifer
Jr. Seau - future hall-of-famer, 16 or 17 years experience before coming to Patriots, playing in 3-4 under BB disciple Nick Saban.
TBC - backup who became a starter only after an injury to Seau, and only in his 5th year in the league.
Chad Brown, Monty Beisel - experienced free-agent pickups, neither worked out but that doesn't change BB's philosophy.
(Did I miss anyone?)
Anyway, by now you should be seeing a pattern here. That's not to say the BB won't use a high draft pick on a linebacker, but it would have to be a guy who BB feels is exceptional in many ways, including his ability to fit into our system.