Your mother his Mitski (Bakugo's mother) met via the fashion industry, his Mitski being the fashion designer and your mother being one of her models. You two had basically been forced on a playdate because they wanted to chat

Bakugo: "So what makes you think you can join my hero agency?! I'm the best you know and I'm gonna be better than all might!" he said, hands on his hips.

He was obsessed with playing hero which startled you as your parents were from a yakuza.