Exchange bias is often observed when anti-ferromagnetic and ferromagnetic phases coexist. The coexistence of two competing magnetic phases can persist to the lowest temperatures if the disorder-broadened 1st order transition separating them is interrupted, as is proposed in the kinetic arrest phenomenon. The fractions of coexisting phases can, in this phenomenon, be tuned by following different cooling protocols. We discuss predicted behaviours of exchange bias resulting from the kinetic arrest phenomenon. Specifically, for appropriate values of cycling field Hmax and measuring temperature T0 there will be no exchange bias under cooling in zero field, while it will manifest with increasing cooling field, and then saturate.