Please refer to the Terms and Conditions in the solicitation for special details but in general a subcontractor is usually required to carry General Liability and Workers Compensation while a prime contractor will be required to have General Liability and Bonding.
As a subcontractor on a contract you are working directly for the prime contractor. In some instances they may provide bonding for you as a subcontractor and in other instances they may ask that you obtain your own bond.
The individual firm must contact their own personal insurance company for a bond.