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We have performed a search for bursts of gravitational waves associated with the very bright Gamma Ray Burst GRB030329, using the two detectors at the LIGO Hanford Observatory. Our search covered the most sensitive frequency range of the LIGO detectors (approximately 80-2048 Hz), and we specifically targeted signals shorter than 150 ms. Our search algorithm looks for excess correlated power between the two interferometers and thus makes minimal assumptions about the gravitational waveform. We observed no candidates with gravitational wave signal strength larger than a pre-determined threshold. We report frequency dependent upper limits on the strength of the gravitational waves associated with GRB030329. Near the most sensitive frequency region, around 250 Hz, our root-sum-square (RSS) gravitational wave strain sensitivity for optimally polarized bursts was better than h_RSS = 6E-21 Hz^{-1/2}. Our result is comparable to the best published results searching for association between gravitational waves and GRBs.