Bridging the SNAP Gap Act of 2023 This bill expands certain income exclusions and the excess medical expense deduction under the Supplemental Nutrition Assistance Program (SNAP). Specifically, the bill excludes income from children in elementary or secondary schools who are age 21 or younger from income calculations for purposes of determining SNAP eligibility (currently, the exclusion is limited to children who are age 17 or younger). In addition, the bill expands the excess medical expense deduction to include all individuals, rather than only individuals age 60 or older or individuals with disabilities. (The excess medical expense deduction allows for the deduction of certain out-of-pocket medical expenses that exceed $35 per month from income calculations under SNAP.) The bill also specifies that the amount of the deduction must be equal to the premium rate for Medicare medical services, although states may choose to set higher amounts.