Create some (unusual) bike storage in the main triangle of your bike, using straps.
Or, use a more traditional means of extra bike storage, like a basket or carry bags. Also remember that you should have your Bug-Out bag on your back as well.
It’s a good idea to have a two-wheeled bug-out option in addition to a car, truck, motorcycle, walking, etc… You never know what the situation will be like.
Have multiple options ready.