Ideas/Thoughts on how to Board up Bay Window?

Maybe command strips, the velcro style?

Or if you use the vertical boards you could maybe clip/hang them over the top as from the photo it looks flat on top of the windows?

Looks good! It's always tricky trying to adapt to bay windows. I think the vertical boards look good, it better sells the storm shutters visual from the street on the 3 window bay. You can play around and see if you can 'combine' the 4 windows into 2 boarded up windows with slightly thicker foam boards on the outer edges to flatten out the plane. I haven't had great success doing it since the wife likes her natural light so we compromise with hanging heads inside along with some red gel hand prints. The 4 window bay would also be great for projection as well where the 3 bay has a lot of cross trim that would interfere with the effect.

Never underestimate the power of Poster Putty!

And this totally depends on the design of your windows and your siding on your house..... hang them from above the window, on fishing line. You can try to find some edges or corners to hang or hook some fishing line. Then you hot glue the fishing line to the backs of the "boards" in their locations in front of the window. Then you hook/anchor the fishing line below the window. The reason to use this idea, is so the boards move with the wind. They'll be in place, but a good breeze will make them shake and move, getting some natural sounds as they bump the house.

I intend to use the Command Hooks for Xmas lights above and below the windows, and tie the fishing line to them.