Andrew Funk added 15 points for the Bison. Alex Timmerman chipped in 13, Elvin Edmonds IV scored 13 and Andre Screen had 10.
Rice shot 11 for 13 from the foul line.
Bucknell (8-22, 5-13 Patriot League) totaled 52 second-half points, a season high for the team.
Javante McCoy had 23 points for the Terriers (20-11, 11-7). Sukhmail Mathon added 17 points and 13 rebounds. Walter Whyte had 13 points.
The Bison evened the season series against the Terriers. Boston University defeated Bucknell 63-61 on Jan. 1.
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