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.