Unfortunately, Asante is probably gone. BB just doesn't view DB as a position worth sinking big money into, as he feels he can get cheaper FA's and young draft picks to do the job nearly as well. Law, Milloy, Samuel last year, etc. - all big money DB's have been let go. The only way Asante is back next year is he takes a discount to the point where his added value over his replacement is worth the extra cap space (see Rodney). From most accounts, however, it looks like he is ready to cash in.
BB's track record clearly indicates he'd much rather spend on LB in FA than DB. A guy like Dansby or Victor Hobson (IMO he's the one we go after - experienced in the 3-4, can play inside or outside, young but has already had a few good seasons) is where our "big" FA signing will come from.
As for the LB vs. DB in the draft debate, I don't think it's that BB refuses to draft LB's. It's just that he devalues LB's based on the development time they take compared to other positions. That's why, of the few LB prospects he likes, they usually get scooped up right before him - they are great value to everyone else where he considers them average value. For instance, he'll probably rate a guy like Laurinitis as a #20-25 first round pick, but around the late teens, some other team will find great value in him there and snatch him up.