Ryan Frazier added 11 points for the Bison, whose 9-1 record marks their best start since the 2005-06 season. It was Bucknell's fourth consecutive victory.
With the score tied at 8 with 13:16 to go in the first half, Bucknell scored 12 consecutive points to take a 20-8 lead at the 9:31 mark. Bucknell led 41-29 at the break.
La Salle closed to five points at 43-38 on Galloway's 3-pointer 4:05 into the second half. Frazier's 3-pointer made it a nine-point game at 55-46 for Bucknell with 9:33 remaining, and the Bison kept the Explorers at bay.
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.