With more than a little malicious glee, Foreign Service officers in the State Department's bureau of European affairs have been giggling over a cable that Ambassador Richard R. Burt in Bonn sent to Secretary of State George P. Shultz and, personally, to President Reagan after he met Soviet dissident Anatoly Shcharansky at the Glienicke Bridge in Berlin.

It fell to Burt to greet Shcharansky at the bridge in the swap of prisoners held by East and West that led to his freedom last month.

According to diplomats who have read the cable, Burt told his bosses that in the emotion of the moment he gave his presidential cufflinks to the Jewish activist.

"I hope you don't mind," Burt reportedly wrote, adding that the whole episode probably would not have been possible under many a previous American administration.

Burt, 39, used to be the assistant secretary of state for European affairs, a job in which he made many enemies among career diplomats. He is widely regarded by Foreign Service officers as a tireless apple polisher, and the cable to Shultz and Reagan is now cited as Exhibit A.

Shaw-ing the Way . . . Following the recommendations of the President's Commission on Organized Crime, the staff of Rep. Clay Shaw (R-Fla.) has decided to set an example for federal employes and submit to voluntary drug testing. Shaw and his 18 staff members in Washington and Ft. Lauderdale will undergo drug testing as soon as they can figure out how to do it. (There is no mechanism in the House rules for having the test done or for paying for it.) They think that it will cost about $25 per person.

According to Shaw, "I think the Congress and the staff should set the right example. . . for the rest of the country. . . . This is a way the members and staff can make a positive statement that we're drug free, and we're willing to stand up and be counted."

Mother Knows Best . . . The National Press Club this week heard an enlivening example of special interest politics at work. Sen. Phil Gramm (R-Tex.), of Gramm-Rudman-Hollings fame, was describing his Sisyphean efforts to persuade colleagues that Medicare should be modified in the interest of savings. Gramm says that Medicare recipients who, however elderly, are not poor should be required to pay higher premiums for it.

He tangled first and hardest, he said, with Rep. Claude Pepper (D-Fla.) -- who is, at 85, Congress's primary champion of the elderly. He was apparently unmoved by Pepper's objections. But, he said, he couldn't stand up to his mother, whose rejoinder was, "Phil. . . you better listen to that sweet Mr. Pepper and keep your mouth shut."

Gramm has decided that the debate over Medicare is "not winnable."