Flame enchantment cannot be applied with anvil

I tried to enchant a bow with flame in a survival world. It took my levels and the anvil sadly broke (this is obviously working as it should so far), but then I looked in my inventory and the bow did not have the flame enchantment. I then went to a creative world to try to recreate this scenario.  It was quite easy.  The bow cannot get a flame enchantment from an anvil.