When bows are shot in your off-hand, they don't shoot, even when nothing is in the mainhand.
Linked issues
Comments 2

Duplicate of MC-82923 – If you have not, please use the search function in the future, to see if your bug has already been submitted.
[Mojang] Dinnerbone (Nathan Adams) resolved MC-82923 - Bow in Offhand does not work properly as 'Works As Intended'
You can't shoot from the offhand. The animation is wonky for using items unsuccessfully but that's its own bug.