A Washington stenographic firm yesterday pleaded guilty to price fixing as part of an alleged conspiracy to rig the bidding for stenographic services supplied to government agencies.

Prosecutors said that the firm, Hoover Reporting Company Inc., and several unnamed coconspirators worked together to submit noncompetitive bids that force government agencies to pay fixed and artificially high prices for reporting services. The firms record and transcribe proceedings verbatim for federal agencies; such contracts are usually awarded to the lowest bidder.

Prosecutors said the firms received more than $30 million from the government from 1966 to 1976 and additional money for transcripts supplied to the public.

Hoover's board of directors, after negotiations with prosecutors, said in court papers that it was innocent of any wrongdoing, but agreed to plead guilty to the single antitrust violation because of the liklihood the firm would be convicted if the case were brought to trial.

During a hearing yesterday before Judge Joyce Hens Green, Doris Hoover, the firm's president and majority stockholder, also pleaded guilty in a separate case to a misdemeanor charge of false pretenses, stemming from a $150,000 reporting contrct awarded by the National Transportation. Safety Board in 1975.

Green scheduled sentencing for both the form and Hoover for April 21. The maximum penalty for the felony antitrust violation against the company is a $1 million fine. Hoover faces a sentence of up to a $1,000 fine, a year in jail or both on the charge against her.

The U.S. attorney's office here has been supervising a grand jury investigation into charged that five reporting firms may have conspired to overcharge the government for services dating back to 1959, it was disclosed last summer.