Dante's characterization everywhere pretty much lends itself to that assumption. The games, the manga, the anime, the novel... Even in the game that shall not be named, Dante's got a pretty pronounced disregard for the token female beyond some distanced concern. It's a pretty easy to grasp fact that Dante lives a dangerous lifestyle that doesn't allow for too many serious relationships, especially with what happened to his family.
Dante's a wise-ass, an egotist, and a show-off. He's supposed to be cocky, and even I, a dude, have no issue with believing he's a slut who'd sleep with anything that had tits. This entire fic was about getting beyond that, not just on Dante's side but on Trish's as well.
You know why, though? It's because he needs some sort of contact that won't get eviscerated. Dante isn't shallow, he's pretty deeply aware of the fact that anything he touches will probably come to the attention of demonkind as a whole. That aloofness is a pretty solid act in order to keep the underworld from getting the idea that he's got a weakness they can go after to get to him. By not showing serious interest in anything, Dante effectively PROTECTS everything from his enemies.
Don't judge a book by it's cover. Dante's plenty deep if you can get beyond the mask of booze, cheap sex, and wild abandon.