Extra Headcanon/AU notes (for the curious): Inko isn’t aggressive nor is she all that intimidating, she just moms everyone. And that within itself has the makings of a terrifying individual.
She is also extremely determined when she wants to be? Bakugou thought she was just a typical, weak schoolgirl when they met as kids, but Inko was determined to make her stop smoking/getting into so many fights. It was downright terrifying what she could do when she had set her mind on something.
They didn’t really become friends until a couple years after they met, though. Bakugou doesn’t really have a good relationship with her parents, and after one particularly hostile spat, Inko just kinda… showed up at her door. She didn’t ask any questions, just knew, and they ditched school for four days to go up to Hokkaido and be happy.
Bakugou’s fearful respect of her is based on years of Inko somehow knowing everything and multiple cases of her calling/texting/msg-ing Bakugou just as she lights a cigarette or glares at some thugs, despite being nowhere in the vicinity. She is 99% certain that Inko has some sort of secondary psychic sense quirk that keeps her attuned to the people she cares about.
(Also, Bakugou really loves her son, but? She also REALLY wants to kick his ass, because Inko took such good care of her when they were younger and she feels entirely responsible for how her son acts towards Izuku. She probably sees Katsuki’s behavior as a reflection of her own and regrets/wishes she was a parent more like Inko, or something.)