You can go to Home Depot and pick up a mess of bamboo tamato stakes for about 5 bucks. Straighten them and you have arrows.
I do alot of trading, good place to get primitive supplies is paleoplanet.
Wife always jokes that it's amazing how we can trade roadkill for sticks and rocks and both parties walk away happy.
For sinew, hit the local deer cooler during rifle deer season. Years ago I took a trash can with a plastic bag. They filled it up, I did this twice.
You can also get deer skin pieces. Some try to charge, but there are many who will just throw them in a pile for you.
Dried it and you guessed. Traded it for: arrow shafts, feathers, rock for arrowheads, strings, and leather.
A fresh car hit otter was traded off for an osage stave. Now, the otter was over 60" long. Just as long as the stave I traded for.
I got my new bow, 60" osage recurve, 65lbs at 27" in a trade. Allan made me a bow, I made Allan a bow.
Yard sales, goodwill, flea markets, any little store that sells used goods is a good bet. I've found prestine bows for 25 bucks, found a Bear A Riser for 1.50. ****ed it for close to 200 bucks.