Muscala finished with 12 points and 10 boards while Bryan Johnson tallied 17 points, eight rebounds and six assists for the Bison (20-4, 7-1 Patriot League), who won despite not scoring a basket in the final two minutes.
Army (10-13, 3-5) trailed by as much as seven, 35-28, in the second half before cutting the deficit to 52-50 with 4:13 left. But Ayers knocked down a 3-pointer and Johnson converted a trey and a jumper on back-to-back possessions to put Bucknell ahead 60-54.
The Bison went scoreless from that point as Army drew to within two, 60-58, with 1:57 remaining but missed three jumpers in the final minute as Bucknell held on.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.