Tying the string on one end is very common among Native American bows. I've only seen a few NA bowstrings with two loops.
Just use whatever knot you like and then wrap the extra length around the end of the bow. Finish off by tucking the end of the string under the last wrap and pull tight. Some original strings had a short piece of bucksin lace attached to the end....so that the last wrap(s) will hold better.
The extra length has two purposes. One, during dry weather, strings made of sinew or rawhide will shrink. Two, the extra length is needed for grabbing onto the string and tying the knot.