Step 1: Thread the Needle and Tie It On
First, thread a needle. If you don't know how, check out this instructable. You will want about two feet of thread, about the same color as the drawstring.
Next, thread the needle through part of the drawstring, and tie it off.
Now we're ready to start wrapping.
Step 2: Wrap It Up!
Start wrapping the thread around, overlapping to make sure everything is covered.
If you run out of thread like I did halfway through, tie off the remaining thread, then start over a little further down. Be sure to sew through the string a couple times and make sure it's secure.
When you get to the end, tie it off securely and cut any remaining thread. You can wrap it all the way to the end, but I wanted a little bit of frayed string at the end.