In some cases, you can get prescription lenses, which cuts down on the bulkiness of wearing a pair of wraparound shades over your regular eyewear or having to wear contacts while you bike.
A slight advantage, especially since I'm 6'1" and 220 lbs. But alas, I overcame my bulkiness (ok, HUSKY) to consistently beat her... but I can still see the vengeance in her eyes.
Avoid pants with bulky pockets or drawstring waists to avoid bulkiness.
To reduce bulkiness where the unit folds in half, use straight scissors to remove a piece of paper about one inch long from the inside pleat.
Jockey also claims that its ultra light fabric is guaranteed to minimize bulkiness, and most importantly, won't ride up!