Can I still file a bond claim on a school project in the state of Colorado if I do not have a signed contract just a signed estimate and a field work directive?
I'm not aware of any requirement for a formal written contract as a prerequisite to make a payment bond claim on a CO public project. Of course, when making a claim, it's extremely useful to have written proof that there's an agreement to do work, even if that's not necessarily what you'd think of as a formal "contract." Additionally, note that it's absolutely possible to form a binding, written contract when a customer signs documents like estimates and field work directives.
For more information on CO payment bond claims: Colorado Bond Claim Guide and FAQs.
If you'd like to discuss the matter with a Colorado construction lawyer, you can find one here: Top Colorado Construction Lawyers.