Yes, a Bridge phase taxpayer is required to sign the CAP MOU (Memorandum of Understanding).
The Bridge phase is a part of the Compliance Assurance Process (CAP) program, and the same standardized CAP MOU is used for all three phases of the CAP program: CAP, Compliance Maintenance (CM), and Bridge. The CAP MOU sets the expectations and requirements for both the taxpayer and the IRS. Although the Bridge phase has specific conditions where the IRS will not accept disclosures, conduct reviews, or provide letters of assurance, the taxpayer is still required to sign the CAP MOU. This ensures that the taxpayer remains compliant with the overall CAP program requirements and is considered a returning taxpayer when applying for the CAP program in the next application period.
Sources:
IRS FAQ