In my younger days I could ride for miles with no hands. Shooting a pistol in any direction other than directly forward would knock you over immediately and even straight forward could cause a loss of control due to the recoil causing a weight imbalance. You could maybe do it with a .22 but I'll let someone else try it. Here's what I think contributed to her horrible accuracy:
1. If she trains, she trains using a two handed weaver type stance and doesn't do a lot of one handed bullseye style shooting, so she has little idea how recoil is going to affect her balance and control.
2. Shooting right handed and controlling the bike with your left hand is a recipe for disaster. Follow up shots are going to be hard to place on a staionary target, let alone a sentient, moving one. Women are crap at cycling too, (sorry ladies, it's mostly the truth, at least when it comes to balance). Even if we reverse the control set up and she shoots left, steering with the right it's still going to be messy.
3. As soon as she fires, it's chaos. The dog will panic, her kid will panic and her lack of control due to her bike now going in some kind of wavy trajectory only makes the subsequent shots more reckless. She probably banged at least one out unintentionally due to the bike being out of control.
All in all a fecking giant mess and she's lucky it wasn't worse. Hopefully the dog owner sues her as well.