Fishing rods can not be enchanted in Survival Mode when there are no bookshelves present. The fishing rod can be put into the GUI slot, but is unable to receive an enchantment until there is a sufficient amount of bookshelves that will bring the enchantment level to more than 3. Levels 1,2, and 3 are unable to receive an enchantment.
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We're tracking this issue in MC-36937, so this ticket is being resolved and linked as a duplicate.
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I was unable to reproduce see image above