Self-hosted program

Advertise on a website that you are starting out a bug bounty program, define and publish your scope, rules, exceptions, vulnerability disclosure guidelines, and establish a reporting process, an email where researchers can submit the vulnerability details or a web form and you have a bug bounty program.

And maybe you need more: marketing of it to reach researchers, a person for triage management, setting up metrics, integrations with issue tracking and notification systems, role based access control, scope adjustments, background checks and filtering of researchers, etcetera.