Jordis the Sword Maiden is my new companion after spending the first 40 levels exploring with Lydia, getting into fights, watching her take a knee, waiting for her to catch her breath, take a few swings, rinse and repeat.
After a few missions in Solitude, Jordis and I became partners (and Lydia took the long walk home). While working on my smithing and enchantment skills, I made her a delightful ebony bow with a swell fire enchantment. Sadly, she has completely snubbed my efforts. For some reason, she really prefers her clunky old log of a bow.
Can I convince Jordis to at least try the new bow? It's really quite nice. Besides, it matches her new outfit…
Best Answer
That is a bug associated with followers that already have a default bow in their inventory (this is usually the Hunting Bow).
Source: http://uesp.net/wiki/Skyrim:Followers#Follower_Equipment
Source: https://en.uesp.net/wiki/Skyrim_talk:Followers/Archive_3
The Unofficial Skyrim Patch (original / Legendary Edition - PC) / (Special Edition - PC) / (PS4) / (Xbox One) should fix that bug. Related patch note:
Other mods (for the PC) that can also fix the bug are: Follower Hunting Bow Fix, DFB - Disable-Show Follower Bow And Arrows, or Followers Hunting Bow Replacement. The followers overhaul mod, Better Followers also allows you to remove the Hunting Bow from your follower, forcing your follower to use the bow you gave them.