The Chandra X-ray Observatory has revealed X-ray bubbles in the intracluster medium (ICM) of many nearby cooling-flow clusters. The bubbles trace feedback that is thought to couple the central active galactic nucleus (AGN) to the ICM, helping to stabilize cooling flows and govern the evolution of massive galaxies. However, the prevalence and duty cycle of such AGN outbursts is not well understood. To this end, we study how cooling is balanced by bubble heating for complete samples of clusters (the Brightest 55 clusters of galaxies, hereafter B55, and the HIghest X-ray FLUx Galaxy Cluster Sample, HIFLUGCS). We find that the radio luminosity of the central galaxy only exceeds 2.5 × 1030 erg s−1 Hz−1 in cooling-flow clusters. This result implies a connection between the central radio source and the ICM, as expected if AGN feedback is operating. Additionally, we find a duty cycle for radio-mode feedback, the fraction of time that a system possesses bubbles inflated by its central radio source, of ≳69 per cent for the B55 and ≳63 per cent for the HIFLUGCS. These duty cycles are lower limits since some bubbles are likely missed in existing images. We used simulations to constrain the bubble power that might be present and remain undetected in the cooling-flow systems without detected bubbles. Among theses systems, almost all could have significant bubble power. Therefore, our results imply that the duty cycle of AGN outbursts with the potential to heat the gas significantly in cooling-flow clusters is at least 60 per cent and could approach 100 per cent.