How do I get rid of bug spray odor if spilled on clothing?

Depends on the type of material.
Whatever you do, do not put it in a dryer until it's resolved.
I would wash it as usual in a washer. If that doesn't work, soak it a day or two in warm water and lots of laundry soap and vinegar.

Don't use soap. Use detergent. There is a difference. You may have to run them through the washer a couple of times. Joypuly is correct about the dryer. That would cause the residue to bind with the clothing fibers.