Once BB started winning he knew he could only acquire talent via the compensatory draft system. So he put his players in a position to accrue value and then trade them off for picks.
He also knew how to generate sacks with relatively average linemen and linebackers.
He and Scarnecchia developed a system for protecting the pocket for TB without writing big cheques. The biggest name OL players eventually left in FA as well. Logan Mankins never won a SB despite being there from 2005-2013.
Seymour, Vrabel, Johnson, Ty Law and Vince Wilfork were all dealt in their prime. BB won't hang onto an over priced star past their prime.
He also created a culture of winning where the best FAs wanted to go there if only for year at a discount