A new ground-based wide-field extensive air shower array known as the High-Altitude Water Cherenkov (HAWC) Observatory promises a new window to monitoring the $sim$100 GeV gamma-ray sky with the potential for detecting a high energy spectral cutoff in gamma-ray bursts (GRBs). It represents a roughly 15 times sensitivity gain over the previous generation of wide-field gamma-ray air shower instruments and is able to detect the Crab Nebula at high significance ($>$5 $sigma$) with each daily transit. Its wide field-of-view ($sim$2 sr) and $>$95% uptime make it an ideal instrument for detecting GRB emission at $sim$100 GeV with an expectation for observing $sim$1 GRB per year based on existing measurements of GRB emission. An all-sky, self-triggered search for VHE emission produced by GRBs with HAWC has been developed. We present the results of this search on three characteristic GRB emission timescales, 0.2 seconds, 1 second, and 10 seconds, in the first year of the fully-populated HAWC detector which is the most sensitive dataset to date. No significant detections were found, allowing us to place upper limits on the rate of GRBs containing appreciable emission in the $sim$100 GeV band. These constraints exclude previously unexamined parameter space.
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