R Coronae Borealis stars (RCBs) are rare, hydrogen-deficient, carbon-rich supergiant variable stars that are likely the evolved merger products of pairs of CO and He white dwarfs. Only 55 RCB stars are known in our galaxy and their distribution on the sky is weighted heavily by microlensing survey field positions. A less-biased wide-area survey would provide the ability to test competing evolutionary scenarios, understand the population or populations that produce RCBs and constraint their formation rate. The ASAS-3 survey monitored the sky south of declination +28 deg since 2000 to a limiting magnitude of V=14. We searched ASAS-3 for RCB variables using a number of different methods to ensure that the probability of RCB detection was as high as possible and to reduce selection biases based on luminosity, temperature, dust production activity and shell brightness. Candidates whose light curves were visually inspected were pre-selected based on their infrared excesses due to warm dust in their circumstellar shells using the WISE and/or 2MASS catalogues, and criteria on light curve variability. We then acquired spectra of 104 stars to determine their real nature using the SSO/WiFeS spectrograph. We report 21 newly-discovered RCB stars and 2 new DY Per stars. Two previously suspected RCB candidates were also spectroscopically confirmed. Our methods allowed us to extend our detection efficiency to fainter magnitudes that would not have been easily accessible to discovery techniques based only on light curve variability. The overall detection efficiency is about 90% for RCBs with maximum light brighter than V~13. This growing sample is of great value to constrain the peculiar and disparate atmosphere composition of RCBs. Most importantly, we show that the spatial distribution and apparent magnitudes of Galactic RCB stars is consistent with RCBs being part of the Galactic bulge population.