Consider a proposition you've never thought of before, perhaps, "The Yodeling Lords of Darkness reside in the Castle of Pancakes atop Kangaroo Mountain." Granted, you've now heard of this proposition (as of reading this post), but imagine a scenario where you haven't read this post. Now, if you've never entertained such a proposition in your thoughts, then "intuitively," you aren't in a position to believe it. So ~Bp.
However, since you've never entertained this thought, how should you think that B~p? This would be, "The Yodeling Lords of Darkness don't reside in the Castle of Pancakes atop Kangaroo Mountain." But you don't have any opinions about the evil yodelers since you have no thought of them; you perhaps don't even know about the Castle of Pancakes or the Kangaroo Mountain. Now, if there is doxastic closure, you might be thought to implicitly believe all the things entailed by what you explicitly believe, and perhaps there is some obscure hypothetical awareness, within you, of the general possibility of evil yodelers, breakfast-themed fortresses, and mountains named after Australian animals. So perhaps there is some "virtual," subconscious sense in which you have thoughts about these things after all.
But epistemic closure is suspect, and the belief operator is not confined to doxastic logic alone but is of a piece with many a normal epistemic logic. More precisely, the problem of logical omniscience stands atop its own weird mountain in this realm, so to speak, and expresses the problem of doxastic/epistemic closure. So again "intuitively," one need not believe all the formal implications of one's other, noninferential beliefs. And so again, if you never consciously entertain a given proposition, perhaps because said proposition is so random as to never have been filtered out of your inner doxastic aether, it is hard to say that you actively believe or disbelieve in such propositions. But so ~Bp holds even though B~p doesn't, here.
There is a different context in which ~Bp does often go with B~p, however. In terms of linguistic pragmatics rather than logical semantics, if someone says, "I don't believe that [insert some proposition p]," this often carries the pragmatic implication that this person also does actively believe that ~p. For example, if a religious fanatic says, "I don't believe in the Zero-gods," they probably also mean to say, "I believe that religions that worship the Zero-gods are false." So your familiarity with this context might be what is prompting you to question the counterpart moment in doxastic logic. You might be interested in dialogical logic in this connection, then.