I had the same question, so I called Lyman's Customer Service last winter.
BBS-BlackPowder is a petroleum-based product. It's also the best cleaner that I've found for BP.
I use Goex FFg and either Bore Butter or Mink Oil/Tallow from Track of the Wolf (the mink oil liquifies in a hot Arizona summer), lubing my own patches (50 cal., .490 and .495 ball) Both seem to work really well with BBS-BP. It doesn't seem to destroy the seasoning of the barrel, and my cleaning effort and number of patches is minimized. :grin:
I can also tell you what didn't work - Birchwood Casey Black Powder Solvent. I have a bottle if anyone is interested. About as effective as spitting on a fire to remove the fouling.