How do I get Materia Enhanced Longarm's Composite Bow?

Firstly, sorry I know this isn't a new player question but I have no idea where else to put it, I am on the level 50 quest where I need to get this bow, where on earth do I find it? I have been looking everywhere. =(

You can either buy one off the marketboard, with materia melded already in it. Usually people sell the quest weapons that way since they're going to be melded anyway.
OR you can buy all the materials separately (the bow plus the materia and catalysts needed) and ask someone to meld it for you.

That's...about it. Or of course, make and meld the bow yourself if your carpentry is high enough.

This is for the Relic quest right? The basic weapon (without materia) is crafted and thus was rather cheap to buy unmelded on the Market Board, however, players often sell them with the specific materia already attached on the Market Board for this very quest, so that would be your best choice. Failing that, try and ask someone who is able to craft you the bow and then have them meld the materia for you.

You could also level a Disciple of the Hand class to level 50 and meld the materia to the bow yourself, which is technically what the development team had in mind when they made the quest, but naturally, most players don't have the time or patience to bother with that.

After checking your profile on the lodestone and noticing you do not craft, your only options are The Marketboard or pay a Carpenter to create and meld the Bow for you.

Of the two relic weapons I've done so far (BRD bow and NIN daggers) one (the daggers) I found on the MB with the correct materia already on it, and for the other I bought a basic unmelded version and got the requested materia and a couple Carbonized Matter and just asked in /shout if there was a level 50 Carpenter around who could meld them for me. (Market areas of any of the main cities are a good place to ask. Lots of crafters gather wherever a summoning bell and market board are next to each other.)

Make sure you get the right materia, though. The quest tells you what type and level it needs to be. I believe for the bow, it's two heavens' eye materia III. If not already melded, you'll also need two Carbonized Matter (Grade 3) to meld them onto the bow.

I went and bought all the raw materials necessary, then had a friendly FC crafter make the whole thing for me including the melding for me. I even knew about the specs for the materia, because I have eight or nine various types of low level materia sitting in my bags right now! It looks like I did miss the carbonized matter, so I certainly owe her those.