I let mine dry a few days but you can actually just put them in a quart plastic Zip Lok bag in a well lit but not sunny space and let them sprout in that. I put a handful of very damp mix in the bottom of the bag, bury the BB 1/3, seal and line up the bags in a flat under my benches. They usually sprout within a couple of months and some are ready to pot up within 4-6 months or less. Just keep out of direct sun or they will cook!
There is always the exception but a BB generally does not grow roots once it is removed from the plant. It is the new growth which develops the viable roots for the future.