I think that it is clear form the text that they were "out" since they took part in local society parties etc. But there's no mention of a ball, At Mansfield and I think that possibly there was no formal ball as it would have been a pretty big undertaking and I can see Lady B being too lazy and "delicate" to make the arrangements. Of course Mrs N could do it, but I think that if it had happened, it might have been a plot point in hte novel of Fanny being left out while her cousins were launched into society.. and F never going anywhere...Possibly thtey just started going to the Local Assemblies and to balls at friends' houses and Lady B confined herself to just holding dinners and non dancing parties which were less effort.