Let me understand this situation first!
Are you in the construction business and this particular party is a individual sub-contractor? If no, then this is not a problem, you are not generally required to provide the IRS a 1099-Misc for a non-business project say that is performed at your home.
If you are in business and is the sub-contractor a Corporation? If yes, no 1099-Misc is required as IRS does not require 1099-Misc for Inc.!
Now if they are individual sub-contractors or single member LLC's and this is a business, a 1099-Misc is required. Usually, the original contract you signed would have the insurance or bonding information. I would call the Bonding agent and explain your situation and have them provide you the EIN#.
It is a tough situation, I would also get a copy of the bonding insurance prior to engaging any company to perform sub-contracting work for your business, including SSN# for each individual officers if you could.