Here's Conor McGregor in the middle of a serious PR offensive ... because, hours after trying to show a judge he's not a violent monster, he took his adorable family out for a cute bike ride in the park!

Conor -- along with his girlfriend, Dee Devlin, and their adorable son, Conor Jr. -- peddled out into Central Park on Thursday afternoon ... flanked by Conor's security team and entourage.

One of the entourage members is Cian Cowley -- who also appeared in court with Conor on Thursday for participating in the attack on a UFC bus back in April.

After the hearing, Conor told the media he regrets his actions and he's taking the case seriously. 

Conor's facing up to 7 years in prison for the attack -- but, c'mon, you think a judge is gonna look at pics like these and really throw this doting bike-riding family man behind bars??

McGregor is one of the most calculating people on the planet. He knows exactly what he's doing.