how often do girls who rush not get bids?

most of the girls that claim they "didn't get a bid" removed themselves from the process and dropped from recruitment, not the other way around

Yeah the only girls who don't get bids are girls who don't get the chapters they want and then remove themselves from the process OR go to pref round, do not maximize their options (AKA single intentional preference, where if you have 2 chapters to rank the last round, you only rank one hoping that would somehow increase your chances of getting a bid from them) and then end up bidless because of that.

If every PNM stuck it out through recruitment and maximize their options, everyone would get a bid. VERY few girls get dropped from rush completely. You have to be seriously weird or rude or have done something TERRIBLE like kick one of the PROUD puppies and then flipped off Joe Biden.