  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.
