Important question that needs answering.... This "Bike Bag", is that something attached to the bike, or is it something attached to your body?
I ask because you REALLY don't want to carry the gun on your bike. The vast majority of bicyclist assaults I have heard about have involved the victim being knocked off the bike as the first sign they were really under assault. If you are 5 feet from the bike with 2 guys between you and it, then a gun on the bike may as well be in your safe at home for all the good it will do you.
You need a bag or pocket attached to your body and a gun that fits comfortably in that bag or pocket. So you probably want something very small and light, like a Kel-Tec P32, P3-AT, or Ruger LCR. Something light enough and thin enough you don't even notice you have it the vast majority of the time.
Most recent story I heard of was a 65-year-old man that was attacked by three teens. He was separated from his bike and backed against a fence. However, he had a .22lr pistol on him and defended himself successfully with it, injuring one teen and killing another. You don't need a big gun for most biking defense, you just need a gun period.