How do you wash a bomber jacket?

Presuming you mean "leather" bomber jackets: Wash by hand using standard laundry soap and warm water; scrub both the inside and outside, but primarily the inside...this is where the sweat and dirt collects and causes the jacket to smell bad. Then let the jacket air dry (by hanging it up).

Do not put it in a washing machine, if you do, be prepared for some SHRINKAGE.