I carry a bow, two packs of arrows, and a shield. I use the shield if I need to get into a firing position through a path exposed to excessive missile fire (ie approaching a Rhun outpost).

I use the mouse wheel to equip and have never encountered this bug. Selecting shield disables bow; selecting bow disables shield. I've never had to double-select bow to put the shield away (and with no other equippable items this bug would actually make the bow impossible to equip with the mouse wheel).

Are you using hotkeys to equip? What happens if you use the mouse wheel? This is probably a very specific bug, which if we nail it down should make it easy to fix.

I switch my weapons using the mouse wheel, no other buttons. When this bug happens, at first I have a bow and a shield, then I press "fire" and got the message "the shield is too big" and then the bug switches to no weapon at all.

I only use horse-compatible bows. Could that be a factor?

Not sure, as I understand, every bow can use a shield if the shield is small enough. I use Galadhrim bow

I've just found a solution. If I place my bow in the first weapon slot, arrows in the second, then a shield and a weapon I don't have this bug anymore.

That's always how I've done it. Makes sense that I've never encountered the bug. Good troubleshooting, sir!