Option 1, go to the Marketplace. Left side, look for "Item Type". Select "Bows", then search. Look and see if anyone is offering a bow for a longsword.
Option 2... your better option. Once in the Marketplace, click on "Offers" on the upper left. The look for "Add Offer" to the left of that. From there, that screen it should be easy enough to figure out. You can put up any item in your inventory (a Longsword if you have it). Then you can choose to ask for any item in the game in return. Select the bow you want. Then you'll have to wait till someone comes along and makes the trade with you... if they ever do. You can still use the Longsword till it's traded. And you can cancel your trade offer at anytime before someone accepts your trade (if you decided you want to keep it).
Hope all that makes sense and helps!
