If rain is likely on my bike commute I will cover my bag in advance, and keep my rain cape/poncho at hand and ready.
You can see my backpack covered with a plastic trash bag with reflective belt, and my orange cape/poncho tucked between the bag and seat with the bungee straps securing it in place.
After trying to dig the gear out of the bag and then cover the bag after it starts raining, I found this to be a better solution, as out takes only a few seconds to stop, don the cape and get back to riding.
Just thought I'd share.