Bigotry exists in the minds and behaviors of bigots.
If someone has already determined that assertiveness is a bad trait in a woman, being assertive will only hurt you in your interactions with that person. It might be possible to change their mind and cause them to abandon prejudices like this, but a) it's not your job to try, and b) such an effort could easily backfire, since it requires pointing out that those prejudices exist in the first place.
It's critical to remember that when a bigot is in a position of power over the targets of his bigotry, they will be affected by that bigotry with no real way to combat it. That's why we have (frequently insufficient, but still existent) protections against sexual harassment and discrimination in the workplace-- you cannot force a bigot to change his mind, but you can force him to change his behavior by applying influence from above.
Minority groups fight for their rights, sometimes giving their very lives. But no target of prejudice can or should be expected to end that prejudice. Prejudices and stereotypes are not formed as a result of careful reasoning-- quite the opposite. They're a weapon placed in the mind by perpetuators of those prejudices/stereotypes, who likewise themselves probably never gave any serious thought to the matter.
And generally speaking, it's not the best idea to try and grab someone's weapon away when it's pointed at you. You didn't put that weapon in their hands, and it's not your job to take it out. Rather, if they can't or won't put the weapon down themselves, it's up to superior powers to make them.