Question: “Is there a rule on size of shred bins with no sprinkler system in the work place?”
OSHA’s interpretation of “combustible waste materials” is wide, but unless you’re shredding oil rags, there is no specific guidance.
The National Fire Protection Association (NFPA)—where OSHA turns for recommendations on fire safety policy—does have a standard for closed combustible waste containers, but that’s it.
Have a fire extinguisher handy (nearby) and dispose of waste as frequently as possible. Also, you want to make sure the bin(s) is not in near proximity to ignition sources, like open, live electrical, and spark producing machinery. Better still, place such a container outside, away from your infrastructure and isolate it.
If we’re talking about a bunch of printer paper in standard shred/recycle bin, you’ve got nothing to worry about. However, an OSHA inspector that takes issue with your situation can cite the agency’s “General Duty Clause” as a catch all citation, to bring a penalty forward if the situation appears unsafe.