Besides the somewhat nihilistic advice not to carry a bag or not to carry anything valuable, the best way to safely carry a bag is to have a double attachment. There are messenger bags that have a shoulder strap that is worn across the torso (instead of only over one shoulder). In addition, some of the these bags have a belt strap that goes around the belly. It's like a harness.
A thief would literally have to knock you down and take it off from you. A grab and run is simply not possible. Naturally, a backpack with hip belt and sternum strap would be even safer.
Basically, the best way, combining different safety approaches would be to take a Pacsafe bag and add a second belt, which is not difficult.
You will never be totally safe but unless they knock you down or hold you at gunpoint they won't get that bag or its contents.
Till