I'm sure Lydia nagged her mother until she agreed to take her, though I don't think Lydia had to nag her very much - she's her mother's favorite and, I bet, used to getting her own way. And, someone like that, full of "self-consequence" and used to "the attentions of the officers" (ch 9)would have no problem being so forward as to tax Bingley on the subject of a ball. She is quite something, isn't she?