More than 600 miles from the city where he has enjoyed prestige and respect, Washington lawyer William A. Borders Jr. stands trial here tomorrow on charges that he and a Miami federal judge conspired to obtain a $150,000 bribe from two convicted racketeers.

Borders, whose achievements included the presidency of a national association of black lawyers and a seat on the D. C. commission that helps select local judges, was indicted in Miami last December along with U.S. District Judge Alcee L. Hastings. Both men were charged with conspiracy to commit bribery and obstruction of justice.

Attorneys on both sides estimate that the case against Borders, which was moved here after Borders objected to extensive pre-trial publicity in Miami, will take about eight days to present to a jury on the 23rd floor of the federal court building here. Hastings, who has challenged his indictment on constitutional grounds, is expected to stand trial in Miami.

Sources have indicated that character witnesses for Borders may include former attorney general Griffin Bell, who once traveled to Europe with him on a presidential mission, and former heavyweight boxing champion Jersey Joe Walcott, who was subsequently elected sheriff of Camden County, N.J.

The president of the city council here, attorney Marvin S. Arrington, is acting as local counsel for Borders and he is expected to sit at the defense table with Washington defense lawyer John A. Shorter Jr., Borders' lead attorney.

Arrington and Borders both serve on the board of governors of the National Bar Association, an organization of black attorneys. Borders was president of that group in 1980. According to official records here, Borders made a $5,000 contribution to Arrington's election campaign last year.

After the grand jury handed up its indictment in Miami, all the federal judges there said they could not hear the case because it involved Hastings, a fellow member of their court. As a result, Chief Justice Warren E. Burger appointed U.S. District Judge Edward T. Gignoux of Portland, Maine, to preside.

Gignoux, once viewed as a leading contender for a seat on the Supreme Court himself, is held in high regard throughout the federal judiciary. He is particularly respected for his even temperament and his ability to move difficult cases quickly and smoothly.

In 1973, Gignouox presided over contempt hearings of the so-called Chicago Seven defendants and two lawyers who were involved in the stormy and often raucous trial stemming from street riots during the 1968 Democratic National Convention. Gignoux convicted three of the defendants and one of the lawyers.

The grand jury indictment in the Borders case, which followed an investigation approved at the top levels of the Justice Department, alleged a scheme under which Borders, acting as a middleman, would collect $150,000 in bribe money from convicted racketeers Frank and Thomas Romano of Fort Lauderdale.

The indictment said that in return, Hastings, who was appointed to the federal bench in 1969 by President Carter, would reduce prison terms and fines he had imposed on the Romanos in his courtroom.

Borders, a stern but familiar presence in the local courthouse in Washington, allegedly accepted $25,000 last September from an FBI undercover agent posing as one of the Romano brothers. He was arrested on Oct. 9 in an Arlington motel parking lot after he allegedly accepted the remainder of the payoff--$125,000--from the undercover agent.

The FBI, alerted to the alleged scheme by an informant and former client of Borders, secretly taped conversations during the investigation, which was code-named "Apple Eye." Special agent Paul Rico, called out of retirement to pose as Frank Romano and meet with Borders, is expected to be a key prosecution witness at the trial here.

The arrest of Borders stunned members of the Washington legal community. It came just hours before Borders was to be honored at a black-tie gala on the Potomac River cruise ship "Dandy," for his service in 1980 as the president of the National Bar Association.

Borders, whose only public comment on the case has been his formal plea of "not guilty," was released the day after his arrest on $25,000 bond. In addition to conspiracy and obstruction of justice, he is charged with two counts of interstate travel to commit bribery. Each of the charges carries penalties of up to five years in jail or a $10,000 fine, or both.

Following his arrest, Borders temporarily removed himself from the D.C. Judicial Nomination Commission, which helps pick local trial and appellate judges as well as the chief judges of both courts.

Hastings also has denied all charges against him. His attorney, Andrew P Mavrides of Florida, said he plans to monitor the Borders trial for his client. Mavrides declined to say whether Hastings would attend the Borders trial or appear as a witness.