We present results from a search for 21 cm associated HI absorption in a sample of 29 radio sources selected from the Australia Telescope 20 GHz survey. Observations were conducted using the Australia Telescope Compact Array Broadband Backend, with which we can simultaneously look for 21 cm absorption in a redshift range of 0.04 < z < 0.08, with a velocity resolution of 7 km/s . In preparation for future large-scale H I absorption surveys we test a spectral-line finding method based on Bayesian inference. We use this to assign significance to our detections and to determine the best-fitting number of spectral-line components. We find that the automated spectral-line search is limited by residuals in the continuum, both from the band-pass calibration and spectral-ripple subtraction, at spectral-line widths of Deltav_FWHM > 103 km/s . Using this technique we detect two new absorbers and a third, previously known, yielding a 10 per cent detection rate. Of the detections, the spectral-line profiles are consistent with the theory that we are seeing different orientations of the absorbing gas, in both the host galaxy and circumnuclear disc, with respect to our line-of-sight to the source. In order to spatially resolve the spectral-line components in the two new detections, and so verify this conclusion, we require further high-resolution 21 cm observations (~0.01 arcsec) using very long baseline interferometry.