You're attempting to apply human concepts of development to a mythological creature. Stop that. Maybe a young dragon in your world is the equivalent of a human child, but that's probably not the case in the OP's world. In the OP's world a "young" dragon sounds to be the equivalent of a college-age human, seeing as it has moved out of its parents' place and is looking to find its own starting bachelor pad.
To the OP: "mate" doesn't have to be a purely biological or romantic concept for a dragon. It could be a social concept, with certain rules regarding what "counts" and what doesn't. Maybe non-dragons don't count. Maybe anything with a lifespan shorter than 500 years doesn't count. Maybe young dragons are expected to engage in romances with numerous partners (including non-dragons), sowing their wild oats before settling down with a proper mate and hoard. Or maybe the dragon doesn't care how much or little sense it makes to devote their entire life to someone who won't persist for more than a tenth of it (humans fall in love with others suffering from terminal diseases, why can't there be dragon equivalents?). Or maybe bronze dragons don't mate for life: that could be a rumor started by humans because they're too short-lived to see otherwise. They're your dragons in your world. The only lore is the lore that you decide to present to your players.