Oh, I so disagree with @Aaron's assertion that nearest neighbor is the best method. The common ASTER products are in radiance values and as such, are 32 bit floating point. Nearest Neighbor applied to float values will produce bias and artifacts. This is the common bias effect that results in the blocky appearance of DEM's that were reprojected using nearest neighbor resampling.
The negative values, mentioned in the post, are a result of cubic convolution fitting a smooth curve to a local window with a high deviance. Since the algorithm can extrapolate outside of the range of the data then values outside the observed data range can occur, including negative values. This same phenomena can occur with unconstrained splines applied to high deviance data (i.e., extremely different values across small distances). This is not the case with bilinear resampling, which will honor the original data range via a weighted mean of 4 neighboring cells.
The assertion that nearest neighbor will not effect brightness values is just not supported, even with 8 bit integer data which with digital numbers, commonly exhibits a continuous distribution. The nearest neighbor algorithm is really intended for discrete integer data with truncated ranges. Here is ESRI's brief description of the three resampling methods. It sounds appealing that "the values stay exactly the same" but this is exactly what introduces bias.
I believe that bilinear is an appropriate algorithm in this case. However, keep in mind that some degree of smoothing is not an undesirable characteristic and when applied to resampling a continuous distribution is quite inevitable. It is more about the acceptable degree of smoothing. Often cubic convolution obtains a better "fit" to the data but is much more sensitive to outliers than bilinear. There is a trade off and if your preference is cubic but are concerned over negative values you could always truncate the data back to the expected range.