To build a large, optically bright, X-ray selected AGN sample we have correlated the ROSAT-FSC (<IX/29>) catalogue of X-ray sources with the USNO (<I/252>) catalogue limited to objects brighter than O=16.5 and then with the APS (<VII/214>) database. Each of the 3212 coincidences was classified using the slitless Hamburg spectra. 493 objects were found to be extended and 2719 starlike. Using both the extended objects and the galaxies known from published catalogues we built up a sample of 185 galaxies with O(APS)<17.0mag, which are high-probability counterparts of RASS-FSC X-ray sources. 130 galaxies have a redshift from the literature and for another 34 we obtained new spectra. The fraction of Seyfert galaxies in this sample is 20%. To select a corresponding sample of 144 high-probability counterparts among the starlike sources we searched for very blue objects in an APS-based color-magnitude diagram. Forty-one were already known AGN and for another 91 objects we obtained new spectra, yielding 42 new AGN, increasing their number in the sample to 83. This confirms that surveys of bright QSOs are still significantly incomplete. On the other hand we find that, at a flux limit of 0.02ct/s and at this magnitude, only 40% of all QSOs are detected by ROSAT.