Bows created by reparing in grindstone are not taken by the recipe book into the crafting grid. - not expected
Crafted bows or bows dropped from sceletons with full durability are taken by the recipe book. - expected
Enchanted and/or damaged bows can create dispenser too, but are not taken by the recipe book. - they should be taken by the recipe book, or not able to create dispenser by manual crafting for consistency
Thank you for your report!
We're actually already tracking this issue in MC-125880, so I resolved and linked this ticket as a duplicate.
If you would like to add a vote and any extra information to the main ticket it would be appreciated.
If you haven't already, you might like to make use of the search feature in the future to see if the issue has already been reported.