Medicaid Women's Basic Health Coverage Act of 1999 - Amends title XIX (Medicaid) of the Social Security Act (SSA) to provide State Medicaid coverage of: (1) screening mammographies for women age 35 and older conducted in accordance with the frequency guidelines established by the Omnibus Budget Reconciliation Act of 1990 for coverage of screening mammographies under the Medicare program (SSA title XVIII); and (2) screening pap smears.