I'm not so sure, unless you know BB is a pushover. It doesn't really hurt him to call here, and if he suspects you of pushing a wide range (which you have to be doing) I think his minimum calling range is getting close to break-even (he should be calling around top 80% if he thinks you're pushing any two).

Of course, it's a big assumption that he'll put that much though into it, but I've seen big stacks call here with pretty terrible (relatively) hands. What happened on your BB the hand before (I'd have been looking for an opportunity to get in there, personally)?