The University of Georgia student whose mug shot went viral says guys are moving faster than cops allege she was when they pulled her over ... claiming she's got dozens in her DMs -- ranging from corny young dudes to old creeps.

We spoke with Lily Stewart -- the blonde bombshell who was thrust into the spotlight when a picture of her flashing her pearly whites after her arrest received a ton of attention online ... and, she tells us gross old men and Casanovas are shooting their shot in the DMs.

Among the ones she's received ... Lily says dudes are saying things like they'll pay her bail and adding puns like "Love is fast, let's move fast."

LS says she's not replying to many of the messages ... but, she's taking them all in stride -- laughing at the funny ones and trying to ignore all the others.

Lily's mom was none too happy about her getting arrested BTW ... 'cause Lily says she's worried it could mess with her future. Stewart adds she plans on slowing down in the future -- so, don't expect another Miss America mug shot down the line.

Stewart -- who was going to a friend's birthday party when she was arrested -- says people are recognizing her on campus now from the viral fame ... though she claims she's got no interest in parlaying this moment into more fame.

Lily also gives us a play-by-play on the arrest ... check out the clip to hear all about what went down from her perspective.

Sounds like Lily's dating prospects are zooming in ... even if she's curbing all of them.