Among the about one dozen luminous X-ray bursters in the cores of globular clusters, only three have optical/UV counterparts unambiguously identified. We have observed two of these counterparts spectroscopically with the low-resolution optical and UV gratings of the Faint Object Spectrograph (FOS) aboard the Hubble Space Telescope (HST), yielding broad (1150-2500 and 3600-7000 Angstrom) wavelength coverage in each case, For the counterpart AC 211 to tbe X-ray source in NGC 7078/M15, our small-aperture FOS data reveal both strong absorption and emission features, as well as a broad spectral energy distribution (SED), that are akin to those determined from earlier ground-based and IUE spectra, but with some important differences. These differences suggest that only the HST spectra of AC 211 are free of significant contamination from nearby cluster stars. Our FOS data for the counterpart ''Star S'' in NGC 6712 permit an investigation of the SED for this second object as well; in this case a composite (and/or variable) SED is indicated. However, intriguingly in the case of Star S, we find little evidence for ally identifiable features-emission or absorption-attributable to the system, although features as strong as those seen for AC 211 would be readily detected. These HST optical and UV spectra of AC 211 and Star S may presage a spectral diversity among the counterparts to X-ray bursters in globular-cluster cores.