Bechtel became an Eagle Scout in 1940, and has been recognized by the Boy Scouts of America with both the Distinguished Eagle Scout Award and the Silver Buffalo Award. Stephen's uncle Kenneth K. Bechtel was awarded the Silver Buffalo in 1950 and served as National President of the Boy Scouts of America from 1956–1959.

Stephen Bechtel attended Purdue University, where he was a member of Beta Theta Pi, receiving a Bachelor of Science degree in civil engineering in 1946. He earned his Master of Business Administration degree from the Stanford Graduate School of Business in 1948.

Bechtel was elected a Fellow of the American Academy of Arts and Sciences in 1990. He was elevated to National Honor Member by Chi Epsilon, the national civil engineering honor society, in 1990. In 1998 Stephen and his son Riley were presented with the Honor Award from the National Building Museum for their company's contributions to the built environment. Bechtel received the Award of Excellence from Engineering News-Record for his leadership of Bechtel Corporation.

The BSA acquired new property near Beckley, West Virginia for a new high adventure base in 2009. Bechtel donated $50 million towards the new base which has been named The Summit Bechtel Family National Scout Reserve.

Lyndon B. Johnson appointed Bechtel to the President’s Committee on Urban Housing. Richard Nixon named him to membership on the National Industrial Pollution Control Council, the National Commission on Productivity, the Labor Management Advisory Committee, and the National Commission for Industrial Peace. Gerald Ford asked Bechtel to serve on the President’s Labor-Management Committee.