BP = before
present, used with distant dates such as 50 000 BP. When used with
radiocarbon dates, which don't go back that far, it is necessary to fix a 'present': so it means 1950.
BP = British Pharmacopoeia. On packets of drugs in Britain the active ingredients are named as e.g. aspirin BP, meaning that this is the name it's officially known to British pharmacists as.
BP = British Petroleum
Bp = Bishop, but only real ones, not chess ones.
bp = birthplace; or boiling point; or blood pressure; or base pairs (i.e. distance along a stretch of DNA)
bp or b/p or B/P = bills payable