We carry out a direct search for bar-like non-circular flows in intermediate-inclination, gas-rich disk galaxies with a range of morphological types and photometric bar classifications from the first data release (DR1) of the CALIFA survey. We use th
e DiskFit algorithm to apply rotation only and bisymmetric flow models to H$alpha$ velocity fields for 49/100 CALIFA DR1 systems that meet our selection criteria. We find satisfactory fits for a final sample of 37 systems. DiskFit is sensitive to the radial or tangential components of a bar-like flow with amplitudes greater than $15,$km$,$s$^{-1}$ across at least two independent radial bins in the fit, or ~2.25 kpc at the characteristic final sample distance of ~75 Mpc. The velocity fields of 25/37 $(67.6^{+6.6}_{-8.5}%)$ galaxies are best characterized by pure rotation, although only 17/25 $(68.0^{+7.7}_{-10.4}%)$ of them have sufficient H$alpha$ emission near the galaxy centre to afford a search for non-circular flows. We detect non-circular flows in the remaining 12/37 $(32.4^{+8.5}_{-6.6}%)$ galaxies. We conclude that the non-circular flows detected in 11/12 $(91.7^{+2.8}_{-14.9}%)$ systems stem from bars. Galaxies with intermediate (AB) bars are largely undetected, and our detection thresholds therefore represent upper limits to the amplitude of the non-circular flows therein. We find 2/23 $(8.7^{+9.6}_{-2.9}%)$ galaxies that show non-circular motions consistent with a bar-like flow, yet no photometric bar is evident. This suggests that in ~10% of galaxies either the existence of a bar may be missed completely in photometry or other processes may drive bar-like flows and thus secular galaxy evolution.
