Changing-look (CL) AGN are unique probes of accretion onto supermassive black holes (SMBHs), especially when simultaneous observations in complementary wavebands allow investigations into the properties of their accretion flows. We present the results of a search for CL behaviour in 412 Swift-BAT detected AGN with multiple epochs of optical spectroscopy from the BAT AGN Spectroscopic Survey (BASS). 125 of these AGN also have 14-195 keV ultra-hard X-ray light curves from Swift-BAT which are contemporaneous with the epochs of optical spectroscopy. Eight CL events are presented for the first time, where the appearance or disappearance of broad Balmer line emission leads to a change in the observed Seyfert type classification. Combining with known events from the literature, 21 AGN from BASS are now known to display CL behaviour. Nine CL events have 14-195 keV data available, and five of these CL events can be associated with significant changes in their 14-195 keV flux from BAT. The ultra-hard X-ray flux is less affected by obscuration and so these changes in the 14-195 keV band suggest that the majority of our CL events are not due to changes in line-of-sight obscuration. We derive a CL rate of 0.7-6.2 per cent on 10-25 yr time-scales, and show that many transitions happen within at most a few years. Our results motivate further multiwavelength observations with higher cadence to better understand the variability physics of accretion onto SMBHs.