We present an efficient, bright, and robust source of photons at the rubidium D1-line (795 nm) with a narrow bandwidth of δ = 226(1) MHz. The source is based on non-degenerate, cavity-enhanced spontaneous parametric down-conversion in a monolithic optical parametric oscillator far below threshold. The setup allows for efficient coupling to single mode fibers. A heralding efficiency of η heralded = 45(5) % is achieved, and the uncorrected number of detected photon pairs is 3.8×10 3 cts/(s mW). For pair generation rates up to 0.5 MHz, the source emits heralded single photons with negligible contamination from higher photon number states as evidenced by g(2) c < 0.01. The source is intrinsically stable due to the monolithic configuration. Frequency drifts are on the order of δ /20 per hour even without active stabilization. By applying mechanical strain, the source frequency can be fine-tuned within a range of ≥ 2 GHz.