HI Alison,
The B1 screening can be run directly via transaction /n/SAPSLL/SPL_CHSB1LO (or /SAPSLL/SPL_CHSB1MLO for batch job) and also as you have already determined you can run the B1 screening from the Blocked Partner transactions (/SAPSLL/SPL_BLBPLO).
KBA 1454104 - (KBA: Scenarios for sanctioned party list (SPL) screening in Global
Trade Services (GTS))lists the screening scenarios and transaction, this might be helpful to you.
Kind Regards
Ann Marie