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.
Chattanooga women's basketball coach Jim Foster has received a one-year contract extension, the same day the school gave the men's coach a two-year extension.
With his floor general gone to the NBA, Kentucky coach John Calipari is using this offseason to improve his physical condition.
Chattanooga men's basketball coach Matt McCall has received a two-year contract extension after leading the Mocs to an NCAA tournament appearance in his debut season.