You need a specific bow enchantment to set things on fire: The Flame enchantmentThe Flame enchantment.
The enchantmentenchantment you get on an item is going to be randomly chosenrandomly chosen, so you'll just have to keep trying until you get a bow that has one. It should be noted that the probability of getting the Flame enchantment on a bow is fairly low, and if the modified enchantment level is less than 19 it is impossible to get.
If you are in creative, you can look up the enchanted book with the Flame enchantment, and with a normal bow, combine them in an anvil, and you get the flaming bow...