We present five new outbursting AM CVn systems and one candidate discovered as part of an ongoing search for such systems using the Palomar Transient Factory (PTF). This is the first large- area, systematic search for AM CVn systems using only large- amplitude photometric variability to select candidates. Three of the confirmed systems and the candidate system were discovered as part of the PTF transient search. Two systems were found as part of a search for outbursts through the PTF photometric data base. We discuss the observed characteristics of each of these systems, including the orbital periods of two systems. We also consider the position of these systems, selected in a colour- independent survey, in colour-colour space and compare to systems selected solely by their colours. We find that the colours of our newly discovered systems do not differ significantly from those of previously known systems, but significant errors preclude a definitive answer.