A U.S. District Court judge denied bond yesterday to John W. Hinckley Jr., the man accused of the attempted assassination of President Reagan and the wounding of three others.

Judge Barrington D. Parker also rejected a suggestion from Hinckley's defense lawyer, Vincent J. Fuller, that Hinckley be confined to a private mental institution while he awaits trial.

The focus of the hearing was Fuller's request that Hinckley, who is currently being held in isolation at the Fort Meade, Md., stockade, be released on personal recognizance and placed in the custody of his parents, who live in an exclusive suburb of Denver.

Parker said his decision to deny bond to Hinckley, who did not attend the hearing, was based on several factors, including the seriousness of the charges against him, his long unemployment and his lack of financial resources.

Parker also said that he could not argue with the government's repeated allegation that Hinckley has a "rootless background" and has spent the last several years roaming around the country, using aliases and often keeping his whereabouts secret from his family.

The government had argued that all those factors contributed to the likelihood that Hinckley would flee from prosecution if he was released on bond. Under federal law, the risk that a defendant will fail to show up in court is the sole factor a judge can consider in setting bond.

Parker said yesterday, however, that "there are no conditions which the court finds reasonable or satisfactory to allow the defendant to be released."

Fuller refused to comment yesterday when asked if he intended to appeal Parker's decision.

Meanwhile, prosecution and defense lawyers have agreed that deputy marshals guarding Hinckley will not read notes and memos that Hinckley has kept in a folder in his cell labeled "Attorney-Client." The government has also agreed to provide defense lawyers with copies of any other writings it may seize from Hinckley's cells.

Defense lawyers had protested that prison guards read Hinckley's private papers, in violation of his constitutional rights, while he was incarcerated at the federal correctional institution at Butner, N.C.