Hermione as a 'bad girl' might be sassy and not afraid to speak her mind to Draco. She could be quick - witted in her comebacks and not let Draco's snide remarks get to her. For example, she might use her intelligence not just for academic purposes but also to outwit Draco in their verbal sparring. She could also be a bit of a rule - breaker, like sneaking out at night or getting involved in activities that are frowned upon in the wizarding world just to prove a point or because she believes in a different way of doing things.
She could be rebellious. Maybe she doesn't follow the school rules as strictly as in the original books and is more likely to take risks.