Butter both sides of bread slices. Place 2 slices pepper jack cheese on each bread slice. Sprinkle crumbled blue cheese over 1 slice. Place on grill; cover and grill until cheeses melt.
Place bacon pieces on bread with blue cheese; top the bacon with apple slices. Top the bacon side with the remaining slice of bread. Grill, covered, a few moments. Remove from grill; let rest briefly. Halve sandwich on the diagonal.