(Abridged:) We present the identification of optical counterparts to 23 Galactic Bulge Survey X-ray sources. We report their accurate coordinates and optical spectra acquired at the VLT and Magellan. All sources are classified as accreting binaries according to their emission line characteristics. To distinguish accreting binaries from chromospherically active objects we develop and explain criteria based on Halpha and HeI 5786,6678 emission line properties available in the literature. The spectroscopic properties and photometric variability of all the objects are discussed and a classification of the source is given where possible. Among the 23 systems, at least 9 of them show an accretion-dominated optical spectrum (CX28, CX63, CX70, CX128, CX142, CX207, CX522, CX794, CX1011) and another 6 show photospheric lines from a late-type donor star in addition to accretion disc emission (CX44, CX93, CX137, CX154, CX377 and CX1004) indicating that they are probably accreting binaries in quiescence or in a low accretion rate state. Two sources are confirmed to be eclipsing: CX207 and CX794. CX207 shows a broad asymmetric Halpha profile blue-shifted by >300 km/s. Such line profile characteristics are consistent with a magnetic (Polar) CV. CX794 is an eclipsing nova-like CV in the period gap. Time-resolved photometry and the large broadening of the Halpha emission lines in CX446 (2100 km/s FWHM) suggest that this is also an eclipsing or high-inclination accreting binary. Finally, the low-accretion rate source CX1004 shows a double-peaked Halpha profile with a FWHM of 2100 km/s. This supports a high inclination or even eclipsing system. Whether the compact object is a white dwarf in an eclipsing CV or a black hole primary in a high-inclination LMXB remains to be established.
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