My phone slips into a can cozy (the flat type that has the folded bottom) and then into a jersey pocket. This protects against sweat and provides minimal cushioning that I hope I'll never need. I can get to it easier (one handed) than if it's in a bag (two hands). The zip lock is in my saddle bag if needed.
"Can cozy" that's a pretty good idea. I'll give that a shot.
I keep my screen facing away when it's in my pocket or jersey. I've dialed 911 a couple of times by accident through my clothing...