Can a business open a tenant security deposit account...Jim Smith Tenant Security Deposit account for ABC Co., with Bob Jones as the signer certifying the Tin for ABC co? I am thinking that they can't but can't find anything supporting my thoughts.

Could you elaborate a little more on who's who in this transaction? The way I read this is that Bob Jones rents space from Jim Smith, where Bob runs ABC Co. Am I understanding correctly?

Yes, that is correct. Jim is the landlord and ABC Co. is the tenant.

You can title this the same way you title your other tenant escrow accounts. The only difference here is that the tenant happens to be a business instead of an individual. Regarding the TIN certification, it makes perfect sense for the business principal to sign. So I think you're in good shape, here.