I've never tried BB's but I have loaded #8 and #7-1/2 shot in .44mag cases for both the magnum and specials. I use Blue Dot mostly, varying charges depending on how much bang, smoke and flash I want, under a .45 caliber BP wool wad with shot to the brim, packed down a little, then a .45 caliber card wad and heavy roll crimp to hold it all together. I used to use Gulf wax to seal the top cover-wads for a while before I figured out it wasn't really necessary as long as I didn't try to store them too long. The powder-over-wad I use is from Ox-Yoke, the DRY Wonder Wads, and they are smokeless powder friendly. Unless you decide to use black powder - which is definitely an option - be careful about using the pre-lubed Wonder Lube wads (registered trademark?). I haven't tried them over smokeless but it occurs to me they may not be quite as smokeless powder friendly. They're definitely nice over FFg/FFFg.
Oh, and I don't use this load for birds so I can't say if it has enough oomph! but it's good for rats and snakes. And spiders. We get BIG spiders down here along the coast and it spatters them nicely. Hope this helps.