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I first found this 3-bead technique in a special Interweave publication, Jean Campbell's "Beaded Cords, Chains, Straps and Fringe," and I've used it ever since.
I work with nine to ten feet of thread doubled to four and a half to five feet, so I don't have to add a new thread. And, yes, it can be aggravating in the first few rows, but I deal with it.
The beginning:
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Bring the needle through the first two beads on the thread as shown. Pull the thread until the last bead added (#4) is sitting on top of bead #3.
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(I flip the beads in my hand after each step so that I'm always moving the needle from right to left. There's no real reason for this except that I can work faster this way.) Pick up a bead and take the needle through the center bead and the #3 bead below the bead on the left. Pull the thread to bring the needles into position. You'll note that there's now a space in the middle.
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The Rest of the Story:
I think of the three steps as Straight, Down, and Across. (Remember that I flip the strip with my left thumb as I pick up the next bead with my right, so I'm always moving my needle from right to left. It's all part of the rhythm.)
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I continue with Straight, Down and Across until the base is the desired length without the clasp.