Bell opened the scoring with an 8-yard TD run in the first quarter and then added three 1-yard scores in the second quarter to put the Sooners (4-1, 2-1 Big 12) on the road to their second consecutive victory.
Damien Williams ran for 167 yards and a touchdown to lead the Oklahoma ground game, which churned up 343 total yards.
The Sooners defense held Texas (4-2, 1-2) to 74 rushing yards and did not give up an offensive score until Mike Davis caught a 44-yard TD pass from Case McCoy with 4:43 remained in the game.
Davis' TD catch came after the Longhorns had scraped together eight points a safety and interception return for a score by Carrington Byndom.
McCoy completed 5-of-8 passes for 102 yards and two touchdowns. David Ash was 13-of-29 for 113 yards and was intercepted twice.