Barbara A. Bowman, a former Senate post office employe and niece of Senate Minority Leader Robert C. Byrd (D-W. Va.), pleaded guilty in federal court yesterday to one count of covering up her embezzlement of post office funds.

Bowman, 44, who lives in Fairfax, had been charged last week with stealing $12,000 from the Senate post office, where she became chief clerk in September 1980. Bowman admitted in a statement to Senate Sergeant-at-Arms Howard S. Liebengood in early August that she took the money, according to Assistant U.S. Attorney Raymond Banoun.

The government alleged that Bowman used the money for personal expenses, including rent.

Liebengood, whose office oversees the Senate post office, has said he allowed Bowman to remain on the job, however, because she was "cooperating" with investigators. He said he accepted her resignation from the $24,000-a-year job early this month after government auditors discovered additional money missing from the post office.

Prosecutor Banoun said in court yesterday that, in exchange for Bowman's guilty plea, the government will dismiss a theft charge against her at the time of sentencing.

Bowman, who had exclusive control over a $20,000 cash bank at the Senate post office, pleaded guilty yesterday to temporarily adding $2,000 to that bank to hide a shortfall in funds from General Accounting Office auditors. Bowman obtained the cash by writing $1,000 checks to each of two employes, according to the government's evidence. She later withdrew the $2,000 and gave the cash back to the employes, who then tore up the checks, the government said.

U.S. District Judge Louis F. Oberdorfer scheduled sentencing for October 23. Bowman faces up to five years in jail a $10,000 fine, or both, on the charge.