Contractor for a project with the City of Los Angeles. There were several change orders that increased the expenses and the City is unwilling to pay.
To answer the question in the title of this post, a claim on a contractor's license bond is different from a claim on a public works' payment/performance bond. Subcontractors or suppliers on public works projects may proceed with claims on payment bonds when they remain unpaid, but they may or may not have a right to assert a claim on a license bond depending on whether there is a sufficient basis to make such a claim under the California Business and Professions Code. The road to recovery for direct (general) contractors is different.