Robert Muse Bass was born in 1948 in Fort Worth, Texas. His Father, Perry Richardson Bass, was an heir and investor. His mother, Nancy Lee Bass, was a philanthropist. He has three brothers Lee Marshall Bass, Ed Bass and Sid Bass. His uncle is Sid Richardson

Bass's Father founded Bass Brothers Enterprises in 1960 after inheriting $11 million from their great uncle Sid W. Richardson in 1959. In 1985, he founded the Robert M. Bass Group as his person investment company. Additionally, Bass serves as the chairman of Aerion Corporation and President of Keystone, Inc. He founded Oak Hill Capital Partners in 1986.

Taft Broadcasting was purchased by TFBA Limited Partnership, which included Robert M. Bass, in April 1987 for $1.43 billion taking the company private. Bass in March 1988 sold the Plaza Hotel to Donald Trump thanks to their mutual friend Thomas J. Barrack Jr.. He led a buy out Bell & Howell in April 1988. In June 1988, Bass made an offer to purchase Macmillan Inc., the publishing and information company, but the company responded with a restructuring.

Bass and his wife Anne donated $13 million to fund the renovation of Yale's Cross Campus Library, which was renamed the Bass Library. In 2005, they donated $30 million to the Stanford Graduate School of Business. In 2013, they donated $50 million to Duke University to support Bass Connections, an initiative to encourage cross disciplinary collaboration and studies. In 2001, Bass and his wife donated $10 million to Duke to strengthen undergraduate teaching. They also donated $10 million in 1996 to establish the Bass Society of Fellows at Duke.

Bass is past chairman of Stanford University's board of trustees, Stanford Management Company, the National Trust for Historic Preservation, and Cook Children’s Medical Center. He is a trustee of Stanford University, a Director of Stanford Management Company, a trustee of the Brookings Institution, a trustee of Rockefeller University, Groton School, Middlesex School, and the Amon Carter Museum.