The low-mass X-ray binary (LMXB) X1832-330 in NGC 6652 is one of 12 bright, or transient, X-ray sources to have been discovered in globular clusters. We report on a serendipitous ASCA observation of this globular cluster LMXB, during which a type I burst was detected and the persistent, nonburst emission of the source was at its brightest level recorded to date. No orbital modulation was detected, which argues against a high inclination for the X1832-330 system. The spectrum of the persistent emission can be fitted with a power law plus a partial covering absorber, although other models are not ruled out. Our time-resolved spectral analysis through the burst shows, for the first time, clear evidence for spectral cooling from kT = 2.4 ± 0.6 keV to kT = 1.0 ± 0.1 keV during the decay. The measured peak flux during the burst is ~10% of the Eddington luminosity for a 1.4 M☉ neutron star. These quantities are characteristic of a type I burst, in the context of the relatively low quiescent luminosity of X1832-330.