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I don't think you need a DSB, exactly. They do burrow into the sand and hide there with their little...tentacle...nose-like thing sticking out. But a few inches of sand should suffice.
I currently have a 2" sand bed with 3 Nassaruis snails. The only time they come out is at feeding time or to lay eggs on my glass. But i think 3-4" is probably perfect
the whole idea behind having those snails is to eat dead matter/uneaten food and help stir the sand. With a bb - i'd imagine any shrimp or fish would just eat any uneaten food left behind - unless somehow it was unreachable under a rock - and even then I don't see how a snail would reach it.
Anyways - I'd say skip the nass snails if you have a BB and go with some other invert that likes leftover meals.