Born and raised in the Lincoln Heights neighborhood of Los Angeles, Riggs was one of six children of Agnes (Jones) and Gideon Wright Riggs, a minister. He was an excellent table tennis player as a boy and when he began playing tennis at age eleven, he was quickly befriended and then coached by Esther Bartosh, who was the third-ranking woman player in Los Angeles. Depending entirely on speed and ball control, he soon began to win boys (through 15 years old) and then juniors (through 18 years old) tournaments. Although it is sometimes said that Riggs was one of the great tennis players nurtured at the Los Angeles Tennis Club by Perry T. Jones and the Southern California Tennis Association, Riggs writes in his autobiography that for many years Jones considered Riggs to be too small and not powerful enough to be a top-flight player. (Jack Kramer, however, said in his own autobiography that Jones turned against Riggs "for being a kid hustler".) After initially helping Riggs, Jones then refused to sponsor him at the important Eastern tournaments. With the help of Bartosh and others, Riggs played in various National Tournaments and by the time he was 16 was the fifth-ranked junior player in the United States. The next year he won his first National Championship, winning the National Juniors by beating Joe Hunt in the finals. That same year, 1935, he met Hunt in 17 final-round matches and won all 17 of them.

As a 20-year-old amateur, Riggs was part of the American Davis Cup winning team in 1938. The following year, 1939, he made it to the finals of the French Championships but then won the Wimbledon Championships triple, capturing the singles, the doubles with Elwood Cooke, and mixed doubles with Alice Marble, who also won all three titles. Riggs won $100,000 betting on the triple win, then went on to win the U.S. Championships, earning the World No. 1 amateur ranking for 1939. Riggs won four consecutive singles titles at the Eastern Grass Court Championships between 1937 and 1940. He teamed up with Alice Marble, his Wimbledon co-champion, to win the 1940 U.S. Championships mixed doubles title. In 1941, he won his second U.S. Championships singles title, following which he turned professional. His new career, however, was quickly interrupted by military Service during World War II as an enlisted Navy specialist. During his military Service, Riggs was a cornerstone member of the 1945 league champion 14th Naval District Navy Yard Tennis Team.

As a 21-year-old amateur in 1939, Riggs won Wimbledon, the U.S. National Championships (now U.S. Open), and was runner-up at the French Championships. He was U.S. champion again in 1941, after a runner-up finish the year before.

After the war, as a professional, Riggs won the US Pro titles in 1946, 1947, and 1949, beating Don Budge in all three finals. In the 1946 tour against Budge, Riggs won 24 matches and lost 22, plus 1 match tied at Birmingham, Alabama establishing himself as the best player in the world (source : American Lawn Tennis July 15, 1946, page 34). The next year, according to some sources, he beat Budge again by the same narrow margin. But other sources say that he played Budge infrequently and that his primary tour was against Frank Kovacs, whom he beat 11 matches to 10. Budge had sustained an injury to his right shoulder in a military training exercise during the war and had never fully recovered his earlier flexibility. Now, in 1947, according to Kramer, "Bobby played to Budge's shoulder, lobbed him to death, won the first twelve matches, thirteen out of the first fourteen, and then hung on to beat Budge, twenty-four matches to twenty-two." Kramer himself, however, had a sensational 1947 as an amateur and it is debatable whether he or Riggs was the top player for the year. The players met three times at the end of December on fast indoor courts; Riggs won two of these matches.

On December 26, 1947, Kramer and Riggs embarked on their long tour, beginning with an easy victory by Riggs in front of 15,000 people, who had made their way to Madison Square Garden in New York City in spite of a record snowstorm, that had brought the city to a standstill. On January 16, 1948, Riggs led 8 matches to 6. At the end of 26 matches, Riggs and Kramer had each won 13. By that point, however, Kramer had stepped up his second serve to take advantage of the fast indoor courts they played on and was now able to keep Riggs from advancing to the net. Kramer had also begun the tour by playing a large part of each match from the baseline. Finally realizing that he could only beat Riggs from the net, he changed his style of game and began coming to the net on every point. Riggs was unable to handle Kramer's overwhelming power game. For the rest of the tour Kramer dominated Riggs mercilessly, winning 56 out of the last 63 matches. The final score was 69 victories for Kramer versus 20 for Riggs, the last time an amateur champion had beaten the reigning professional king on their first tour. In many of the last matches, it was assumed by observers that Riggs frequently gave up after falling behind and let Kramer run out the victory. Riggs says in his autobiography that Kramer had made "nearly a hundred thousand dollars ... on the American tour alone, while I took in nearly fifty thousand as my share."

Riggs became famous as a hustler and gambler, when in his 1949 autobiography he wrote that he had made $105,000 ($1,847,000 today) in 1939 by betting on himself to win all three Wimbledon championships: the singles, doubles and mixed doubles. At the time most betting was illegal in England. From an initial $500 bet on his chances of winning the singles competition he eventually won the equivalent of $1.5 million in 2010 dollars. According to Riggs, World War II kept him from taking his winnings out of the country, so that by 1946 after the war had ended, he then had an even larger sum waiting for him in England as it had been increased by interest.

In 1973, Riggs saw an opportunity to both make money and draw attention to the sport of tennis. He came out of retirement to challenge one of the world's greatest female players to a match, claiming that the female game was inferior and that a top female player could not beat him, even at the age of 55. He challenged Margaret Court, 30 years old and the top female player in the world, and they played on May 13, Mother's Day, in Ramona, California. Riggs used his drop shots and lobs to keep an unprepared Court off balance; his easy 6–2, 6–1 victory in less than an hour landed him on the cover of both Sports Illustrated and Time magazine. The match was called the "Mother's Day Massacre".

Riggs was diagnosed with prostate cancer in 1988. He and Lornie Kuhle founded the Bobby Riggs Tennis Club and Museum in Encinitas, California to increase awareness of the disease and house his memoirs/trophies. Riggs died on October 25, 1995, at his home in Leucadia, Encinitas, California, aged 77.

Riggs had originally challenged Billie Jean King, but she had declined. Following Court's loss to Riggs, King accepted his challenge, and the two met in the Houston Astrodome on prime time television on Thursday, September 20, in a match billed as The Battle of the Sexes. The oddsmakers and Writers favored Riggs; he built an early lead, but King won in straight sets (6–4, 6–3, 6–3) for the $100,000 winner-take-all prize.

"Riggs," said Kramer, "was a great champion. He beat Segura. He beat Budge when Don was just a little bit past his peak. On a long tour, as up and down as Vines was, I'm not so sure that Riggs wouldn't have played Elly very close. I'm sure he would have beaten Gonzales — Bobby was too quick, he had too much control for Pancho — and Laver and Rosewall and Hoad."

In the 2017 film adaptation Battle of the Sexes, Riggs was played by Steve Carell, with Emma Stone as Billie Jean King.