Ground push back crew reported aircraft movement at the gate when the aircraft brakes were released due to the tow bar not properly attached to the tug. The crew immediately communicated to set the brakes to the flight deck and then re-attached the tow bar to the tug.

Narrative

We hooked up the towbar before loading the aircraft on [Gate] X and noticed that we did not have a bypass-pin to install. Person A offered to go and retrieve a bypass pin from the Crew Chief's office. Out of an abundance of caution; I removed the main pin connecting the towbar to the pushback tractor; just in case the bypass pin was forgotten later on. We finished loading the flight; closed everything up and started to push and that's when were reminded of the missing pin.As soon as the brakes were released; I noticed the plane slowly rolling and the pushback tractor still parked. This prompted me to immediately give the 'X' signal to the pushback driver and approach him to assist.We were working short with a two-man crew and a Crew Chief. This causes everyone on the crew to accept different roles and responsibilities out of their normal scope. I typically check the towbar before push back no matter the position that I'm in under normal circumstances; but because we were under duress and short-handed; my normal checks were overlooked. The person who loads the bags is usually the DeFacto pushback driver in ZZZ and would be the first person to notice any discrepancies in relation to the towbar. Because we were short a guy; our roles were not clearly defined until it was time to push. I immediately told Person A to set the brakes (which he had already done by the time I got to the tractor) and explained to him what I had done. Once I had verified that that there was no damage; I jacked the towbar back up and assisted in reconnecting it to the aircraft. The gate agent was watching from the jet bridge and was taking pictures of us from above on her cellphone (which she has done on several occasions in the past). After we came in inside; the Crew Chief and myself had a conversation with a customer service manager about the occurrence and told her everything that had transpired. Suggestions: Don't work short. You end up missing details you wouldn't normally overlook because you're stretching yourself too thin and your typical checks may be overlooked. I normally religiously check the towbar before every flight I work and of course; the one time I don't something like this occurs. In retrospect; removing the towbar from the aircraft as well as the pushback tractor would've been an even safer alternative than my approach in just disconnecting it from the pushback.