A system includes a bridge seal assembly configured to form a seal within mineral extraction equipment. The bridge seal assembly includes an annular bridge seal having an accordion-shaped body portion with a plurality of folded portions. Each of the plurality of folded portions extends circumferentially about the annular bridge seal, and the plurality of folded portions are configured to enable the annular bridge seal to expand and contract with the mineral extraction equipment to maintain the seal. The bridge seal assembly also includes a reaction ring and one or more wedge rings configured to be inserted between the annular bridge seal and the reaction ring to actuate the annular bridge seal.