Bamforth had eight points in a 14-2 run beginning the second half for the Wildcats (11-3, 6-0 Big Sky), who have won seven in a row.
The teams played even most of the first half, battling to six lead changes and five ties. The Wildcats led 28-26 at halftime.
Weber State had a 33-20 rebounding advantage for the game, led by Kyle Tresnak with nine.
The Wildcats shot 55.8 percent from the field, making 24 of 43 shots. They were 10 of 20 from behind the 3-point line. The Bengals shot 40 percent and made 2 of 10 from beyond the arc.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.