From this article (
Link), it seems that the stair fall and subsequent altercation was a bit humiliating for Jack, so he walked off in a bit of a huff, without saying goodbye to his female friend smoking outside. I question whether he was romantically interested in her, because this can make people do silly things.
At the point he gets to the Plimsoll Swing Bridge, he seems to have weighed his options on getting home that night and decided to cross back to the other side. Initially the reason seems to not be to say goodbye to his friend, because he is spotted on CCTV heading towards the Clifton Suspension Bridge (away from the party) and possibly to his brother's place. Only when his female friend calls him, does he turn around again heading back towards the party on CCTV, probably to say goodbye properly. But walking to the party should only a 4 minutes from where he is last spotted on CCTV, so how did he not make it back!
There are a few possibilities here. Maybe Jack did make it back to the party and something else happened. Maybe she has a boyfriend, leading to an altercation with him, or giving her a reason to lie about the timescale of events to protect her relationship. Maybe she rejected him which upset him greatly?
Either way, I suspect there is more to this story.