He was a 1206/1600 SAT 566 verbal and 640 math. student and 77/100. To get into Yale, his father was a legacy, and he was politically well-connected and fancy prep school. It was also easier to be accepted in the 1960's. The connections were called affirmative-action policy for children.
At Yale, he was a "C" student, and graduated with BA in History and lowest grades in political science and economics. To get into Harvard Business School had to be by connections using the open quota for affirmative action for diversity. He had been rejected by the University of Texas Law School for lackluster grades at Yale. It certainly wasn't being president of his fraternity, Delta Kappa Epsilon, known as the hardest-drinking jock house at Yale. Bush Sr obviously got him into Harvard, I believe Bush Sr was head of the RNC back then after being a Congressman and Ambassador. GWB as graduate of an Ivy League School paying full tuition and politically connected family was a way into Harvard without grades and test scores. At the time at Harvard Business School, anyone who showed up in class and did any work at all could receive a "low pass" (classes were pass/fail, but there was high pass, pass and low pass). They encouraged study groups and a lot of the exams were take home honor system: you get the question and bring back your answer some number of hours or days later. There is a difference of graduating and being an honor student, especially back at time.
We can take issue with the fact that as President, GWB spoke out against affirmative action programs and diversity at universities stating that students need to earn entry. I guess having rich politically connected family is another earning, regardless of grades.
Add - GWB was never dumb, IQ estimated at about 125 as well above average, just very low ranked among US Presidents.