One problem with asserting that your assertiveness doesn’t indicate bitchiness is that it probably does. If all women know that assertiveness will be perceived as bitchiness then those who are going to be perceived as bitches anyway (due to their actual bitchiness) and those who don’t mind being seen as bitches (and therefore are more likely to be bitches), will be the ones with the lowest costs to speaking up. So mostly the bitches speak, and the stereotype is self-fulfilling.
This model makes it clearer how to proceed. If you want to credibly communicate to the world that women who speak up are not bitches, first you need for the women who speak up to not be bitches. This can happen through any combination of bitches quietening down and non-bitches speaking up. Both are costly for the people involved, so they will need altruism or encouragement from the rest of the anti-stereotype conspiracy. Counterintuitively, not all women should be encouraged to speak more. The removal of such a stereotype should also be somewhat self-fulfilling – as it is reduced, the costs of speaking up decline, and non-bitchy women do it more often.