  The star formation efficiency (SFE) has been shown to vary across different
environments, particularly within galactic starbursts and deep within the
bulges of galaxies. Various quenching mechanisms may be responsible, ranging
from galactic dynamics to feedback from active galactic nuclei (AGN). Here, we
use spatially-resolved observations of warm ionised gas emission lines from the
imaging Fourier transform spectrograph SITELLE at the Canada-France-Hawaii
Telescope (CFHT) and cold molecular gas (CO(2-1)) from the Atacama Large
Millimeter/sub-millimeter Array (ALMA) to study the SFE in the bulge of the
AGN-host galaxy NGC 3169. After distinguishing star-forming regions from
AGN-ionised regions using emission-line ratio diagnostics, we measure
spatially-resolved molecular gas depletion times (\tau_dep = 1/SFE) with a
spatial resolution of \approx 100 pc within a galactocentric radius of 1.8 kpc.
We identify a star-forming ring located at radii 1.25 \pm 0.6 kpc with an
average \tau_dep of 0.3 Gyr. At radii < 0.9 kpc, however, the molecular gas
surface densities and depletion times increase with decreasing radius, the
latter reaching approximately 2.3 Gyr at a radius \approx 500 pc. Based on
analyses of the gas kinematics and comparisons with simulations, we identify
AGN feedback, bulge morphology and dynamics as the possible causes of the
radial profile of SFE observed in the central region of NGC 3169.
