I was told in the past that when you cast the Bound Bow spell and have no arrows, the game spawns 100 Bound Arrows and equips them so you can actually use the bow. However, every time I've cast the spell (with or without arrows in my inventory) they never equip. I've seen them show up in my inventory via console and even equipped them with console but they don't do it on their own. And being bound weapons from a spell, they also don't show up in my inventory (well they do in the console window but not in the actual "player facing" inventory). Is there any way to fix this? Also why does this happen in the first place?
As I recall, this is directly driven by a script. If you have mods installed, double check which ones are overwriting the BoundBowEnchEffect Script, or something named along those lines. The script should have a line or two that controls how many bound arrows are added and equipped when the bow is summoned upon casting the spell, and there are some mods that tweak or overwrite this script to achieve different things. If you have no mods installed, it still might be a good idea to refresh your scripts by extracting them again from Scripts.rar to confirm the scripts are all there and compiled correctly. If you are using SSE, I am not sure how this process might be different, but this would be my first bit of troubleshooting in Skyrim LE. I think the main difference with SSE and LE regarding scripts is the folder structure, so make sure you unpack the archive to the correct place for your installation.