Where can I get durable bows?

There are many many places you can find bows in this game.

• If you have the money, ancient parts, and have completed the quest Robbie's Research, you can buy the Ancient Bow from Cherry at the Akkala Ancient Tech Lab. This is considered one of the most, if not the most, durable bows in the game.
• Another reliable source of bow's that I found was Hinoxes. These lovely things have 3 weapons around their necklace and one of them is always a bow.
• Find monster towers (those wooden platform tower things) and kill em all. Usually one or more will have a bow you can use.
• Once you start getting ambushed by the Yiga clan, the weaker ones will drop a Duplex bow once dispatched.

Time to go Lynel hunting!!

Lynel's have a super cool bow in this game that--for the price of one arrow--will shoot three shots at once! Most Lynels carry this awesome bow on their back and will drop it when killed. Not to mention, they also drop a pretty beefy weapon and sometimes a very nice shield!

The only downside here is the fight itself. Lynels have a crazy amount of health, so fighting them will take some time and will usually break a weapon or two of yours. After I finish a dungeon or am in between tasks in BotW, I'll collect up a bunch of subpar weapons and go sacrifice them into a lynel for their bow, melee weapon and shield. Not to mention, their guts and horns are useful for crafting or selling!

The Lynels in the game can be found in these locations (with the weapons listed by letter):

I've taken this image from this enlightening Reddit post that also includes a little more information in text form in the comments.

If you have trouble defeating them, there are a plethora of online guides for how to handle them (even one right here on Arqade!). Once you get the timing down to flurry rush their attacks, they get a lot easier!