Ramp agent reported a tow bar breakaway from the tug during pushback resulting in uncommanded aircraft movement The aircraft was stopped and there was no injury or damage to the aircraft.

Narrative

I was assigned a flight on Gate X that arrived at around XA:50. when the plane came in; I proceeded to do my walk around and hook up the towbar to the aircraft. I got distracted by the gate checks and went over to pick them up and forgot to lock to properly to the aircraftIdentification: As I started to push the plane second time I noticed that it wasn't turning it as it usually does. I thought it was because of the weather or the pushback I was using. So as I continued to push I noticed that shipping had broke and so did the pilot. He asked me to a break I said yes; and I asked him to set the brakes; and I said the brakes and the manager was notified.Cause: As I started to push; I noticed that the toolbar wasn't properly connected and I slowed down to come to a stop. As I came to a stop; the tour disconnected from the aircraft and I asked the pilot to set the brakes. He said the brakes and I reconnected the toolbar and continue to push.Response: Manager was notified and sober maintenance. They did their maintenance inspection and found out there was no damage to the aircraft and told me to push the plane out.Suggestions: I suggest always double checking and stay vigilant at all times