We present the results of a two and a half year optical photometric monitoring programme covering 16 AM CVn binaries using the Liverpool Telescope on La Palma. We detected outbursts in seven systems, one of which (SDSS J0129) was seen in outburst for the first time. Our study coupled with existing data shows that 1/3 of these helium-rich accreting compact binaries show outbursts. The orbital period of the outbursting systems lies in the range 24–44 min and is remarkably consistent with disc-instability predictions. The characteristics of the outbursts seem to be broadly correlated with their orbital period (and hence mass transfer rate). Systems which have short periods (30 min) tend to exhibit outbursts lasting 1–2 weeks and often show a distinct ‘dip’ in flux shortly after the onset of the burst. We explore the nature of these dips which are also seen in the near-ultraviolet. The longer period bursters show higher amplitude events (5 mag) that can last several months. We have made simulations to estimate how many outbursts we are likely to have missed.