Atmospheric Pressure Plasma Jets have been intensively studied due to their potential application in biological fields but some of their physics properties are still not well understood. In the present article, a helium plasma jet driven by 15–18 kHz sinusoidal voltage ignites multi-periodic self-triggered mode or random mode depending on the applied voltage, driven frequency and inter-electrode gap distance. Most of the observed multiperiodic bullets operate every 2 or 3 sinusoidal periods. Such bullets show similarities with pulsed operating mode, having a jitter of less than 100 ns. The presence of an outer grounded electrode ring is a key parameter permitting the ignition of multiperiodic bullets; it also enhances the propagation length up to 8 times. Fast imaging reveals that 2–3 self-triggered discharges occur in the gap region prior to ignition of the bullet in both positive or negative polarities; this leads to an accumulation of charges beneath the ground electrode, locally enhancing the electric field. Bullet velocities for different polarities and gap distances are compared using optical emission spectrum.