If you own a "messenger bag" that swings forward or moves in any way, while you are riding your bicycle, then it is not a true bicycle messenger bag. Transporting items from one point to another securely, while riding a bicycle, was their primary intent when they came to be.

Modern quality messenger bags as we know them today, (Timbuk2, Chrome, Manhattan Portage, Bailey, R.E. Load, Seagull, Outlaw Earth, Zo, Pac, and others), were specifically designed and built by young men and women who had to depend on them to transport all sorts of items from one point to another, securely, while riding a bicycle for 8 or more hours during the course of a day. These bags should have, not only a main shoulder strap, but also a cross strap that secures the bag comfortably on your back and prevents it from moving. They should be sturdy, water proof, and a well built bag is definitely not cheap. If worn properly, and with a reasonable load, they should be very comfortable to wear.