The organisation needs to raise 400,000 every year to continue to provide free public access, while conserving and building its collection of printing presses, books, typefaces, and trade artifacts.
It launched the Foundation Benefactor scheme at an event attended by leading figures from the printing, publishing, design and typography industries.
BPIF chief executive Michael Johnson was one of those who attended.
"The St Bride Library is unique," Johnson said. "It is one of three centres of its kind in the world. The heart of printing in the modern world today, as in the past, resides at St Brides.
"Our priority within the next year to 18 months has got to be in finding a solution for the library."