Bows cannot to be repaired on anvils. I've tried Onyx and Mythril Bows with no success. However, I seem to be able to repair swords and other tools with no issues.

Sorry Sinhika, the document I read online that mentioned ingots for repair must have been outdated.

I looked into this.

1. Normal repair material for the bows are mithril and onyx rods, for mythril and onyx bows respectively. Note that a vanilla bow cannot be repaired with raw ingredients on an anvil at all.
2. Vanilla bow repair mode on an anvil (damaged bow + bow) also works with Simple Ores bows, though material-wise you're far better off using the rods for repair materials.

In both cases, you retain the enchantments on the leftmost bow when it is repaired.

You are right about that... The SimpleOres Wiki is a bit out-of-date, but, to my surprise, it looks like I have edit priviledges there, so I will update it. I did not think I had edit privs there (it's AleXndr's old wiki)