I must have done it wrong, I drank a potion that increases bow damage by 20% for 60 seconds just seconds before I opened up the enchanting table and it still only enchanted for 40%. Is there a different potion I should use?
There is a potion literally called Fortify Enchanting. Drink that, and for X seconds enchantments you cast will be Y% stronger.
The boost to your Enchanting skill is temporary. Enchantments put on items in the meantime are permanently higher than they would have been if you hadn't drunk the potion.