The teams are tied for seventh in the Mid-Eastern Athletic Conference at 7-9.
Bethune-Cookman (11-20) scored the last 10 points of the first half - including 3-pointers from Trapp and Johnson - and led 36-32 at intermission.
A nine-point spurt for Bethune-Cookman midway through the second half put the Wildcats up 55-44, while South Carolina State went over five minutes scoreless. A seven-point run a little later made it a 13-point lead and the Bulldogs never recovered.
Johnson and Trapp combined to go 7 of 15 from beyond the arc.
Both teams shot better than 50 percent from the floor.