Heather,
I believe it is best to not breed blues and blacks together, if that is what the "bb" stands for. The best blacks will carry gold, while the best splash and blue birds will carry silver. Also, to get the best lacing on blues you will want to breed blue to blue.
Christie started a great topic on this.
For blue birds cull the splash and blue birds that show any gold. Take the best splash (silvery...no gold) male(s) and put him over your best blue (laced if you have any) females. Keep only the pullets from this mating. They will only carry silver, due to it being sex-linked. Use that best splash male over them and all the offspring should be pure for silver.
If you have to go back to an outcross using black be sure to only use black females and then only keep the pullets to breed from in your blue and/or splash project(s). This is also true when an outcross to black is needed to improve size, egg color, feather quality, etc. of lavender strains.