Minecraft repairing Enchanted items

You need to use an anvil and sacrifice some experience levels.

Normally what you do is put the item to be repaired in the first slot and the material its made of (iron, diamonds, etc.) in the second slot. I don't know what the material you need to use for bows is, I haven't been able to find it on the wiki. Because of that, I would combine two bows into one using the anvil, since bows are pretty cheap. At this time you could also add more enchantments to your bow by adding an enchantment to the other bow.

If you do not use the anvil, the enchantments will not be preserved. Good luck!

Although the other answers point you to the anvil which is a good place to be to repair your enchanted tools, there is an important missing.

Repairing your tools is expensive

You can combine multiple tools/weapons/pieces of armor on the anvil to add their durability and enchantments. But doing so increases the XP cost of future repairs. These cost quickly rise to unimaginable hights. I remember having to pay around 30 levels per tool after just a few repairs. In addition to the amount of diamonds for the tool used to repair the original. Taking into account that you want to combine enchanted tools to improve the enchantments on the first one and that combining enchantments is very expensive in XP, this way of repairing is definetly not worth it in the long run.

Mending FTW

You are definetly far better of obtaining a mending enchantment book from villagers (for example) and enchant your tool/weapon/armor at an anvil with this enchantment. Mending directly puts the XP you gather into the durability of your enchanted piece of gear. So you can repair your tools by killing mobs or smelting a lot of stuff, or however you plan to get your XP.

Mending cannot be obtained at an enchantment table, which is why I would recommend to investigate in villager trading to have them sell mending to you.

There is one exception when it comes to enchanting items with mending: A bow can only have either the enchantment "Mending" or the "Infinity" enchantment. Those are mutually exclusive.