If you do not cut your piece off the loom, the warp threads will be continuous and hence, because there is no risk of piercing your warp with your needle, you can pul that warp all the way through cretig four finished edges.
Start pulling from the middle out, which means choose a pair of warp threads and pull it until the opposite end is snug against the beads. Then go to the other end of the weaving and pull on that thread so it's snug against the beads. Your warp is going to get longer and longer and you might want to stop after an inch or so and sew in those ends.
Additional comments from Jane Overman: I usually start in the middle of the bracelet. Put the project on the table flat and start in the middle. Go one direction and then the other. Pull one thread til it's snug against the bead. Follow it down to the other end and pull that thread thru to the opposite end. keep going til all threads are at one end or the other. If you get to a snag and it won't pull easily leave it alone and go to the next thread. (note from Claudia: you can then weave that thread in later)