This paper presents the first results of a survey for bright quasars (V<14.5 and R<15.4) covering the northern hemisphere at Galactic latitudes |b|>30{deg}. The photometric database is derived from the Guide Star and USNO catalogs. Quasars are identified on the basis of their X-ray emission measured in the ROSAT All-Sky Survey. The surface density of quasars brighter than 15.5mag turns out to be (10+/-2)x10^-3^deg^-2^, about 3 times higher than that estimated by the Palomar-Green (PG) survey. The quasar optical luminosity function (LF) at 0.04<z<=0.3 is computed and shown to be consistent with a luminosity-dependent luminosity evolution of the type derived by La Franca & Cristiani (1997AJ....113.1517L) in the range 0.3<z<=2.2. The predictions of semianalytical models of hierarchical structure formation agree remarkably well with the present observations.