the leather on the hudsons are sturdy. i've taken my striping bags out in the pouring rain with no problems. it'll dry completely without leaving any marks, but i understand the worry!
I would be worried (actually, not just worried but freaked out) too if that happened to me but I agree with everyone, MJ bags are built to last Plus it sounds like things are getting better already!
You could always keep a plastic bag folded up in side in case you get caught in the rain. The same thing just happened to me and my chloe edith bag. My thread was Edith AMOST got a bath!! I ran with my bag under my coat like a fool!! That when the girls suggested a plastic bag!!