Schrum graduated from John Foster Dulles High School, near Houston. He received his B.A. in psychology in 1968 from Southwestern University, where he served as president of the Student Government Association. That same year, he enrolled in the Perkins School of Theology at Southern Methodist University. While at SMU, Schrum and his spouse, Jane Woodman Schrum of Houston, served as residence hall parents for approximately 600 first-year male students.

In 1970, the Schrums returned to Southwestern where Schrum served as director of men's housing and associate chaplain. That same year he decided to pursue full-time work in higher education and was encouraged to finish his theological studies at Yale University. He graduated from Yale Divinity School in 1973 with a Master of Divinity degree and immediately began his administrative career with Yale University--first with the Association of Yale Alumni, then with the Yale Alumni Fund. Schrum spent his last few years with Yale as a fundraiser for the Divinity School, playing a minor role in Yale's $370 million campaign (at that time the largest fundraising effort ever attempted by a college or university). At Yale Divinity School he also served as chaplain to the school's United Methodist students.

Schrum left Yale to become director of development at Muhlenberg College in Allentown, Penn. In 1978 he returned to Texas to be the vice president of Texas Wesleyan College. Three years later, Schrum was asked by his alma mater, Southwestern University, to serve as vice president for university relations. As Southwestern's advancement program began earning a national reputation, Schrum was invited to become vice president for development and planning at Emory University. There, he directed the university's last major mega-campaign--the $400 Million Campaign for Emory. In 1991, having served at Emory for more than six years, Schrum was elected the 17th President of Texas Wesleyan University in Ft. Worth.

During his time at Texas Wesleyan, the university's endowment more than doubled from $22 million to $50 million, and the enrollment increased from 1,429 to 3,000 students. The annual fund also doubled from $450,000 to just over $900,000. A law school was acquired and fully accredited by the American Bar Association and a $12 million campus was built for the law school in downtown Fort Worth. A Weekend University, an MBA program, a distance-learning program in graduate education, as well as a bilingual education program also were established. Texas Wesleyan's budget grew from $11 million to $32 million in just eight years, and the university garnered resources amounting to almost $40 million.

In January 2000, Schrum was elected president of Southwestern University. He took office July 1, 2000.

Schrum has served as chair of the Board of the Council for the Advancement and Support of Education (CASE), the world's largest international educational association, and on the Board of the National Association of Independent Colleges and Universities (NAICU), as well as the Foundation for Independent Higher Education. In 1983, while vice president at Southwestern, he completed Harvard's Program in Educational Management. For five years, he was a lecturer in the Harvard University Seminar for New Presidents. He is a frequent lecturer on topics related to the advancement of higher education.

Schrum is an ordained United Methodist minister. He is a member of the Philosophical Society of Texas, National Association of Independent Colleges and Schools, American Council on Education, Independent Colleges and Universities of Texas (immediate past chair), National Collegiate Athletic Association, The Annapolis Group, and National Association of Colleges and Schools of The United Methodist Church.

He also serves on the board of directors of First Texas Bank of Georgetown, Georgetown Project, Southern Collegiate Athletic Conference, Georgetown Area Assistance League (Board of Advisors), Georgetown Area Community Foundation, Southern University Conference (President), Association of Governing Boards (Council of Presidents), Texas Independent College Foundation, Association of Texas Colleges and Universities, Educational & Institutional Insurance Administration, and Associated Colleges of the South (Chair).

Jake and Jane Schrum have two daughters: Libby and Katie.