Any thoughts? Sure; my thought is that it is about equally as likely that Sarah Bunting is in fact King George V's deceased youngest son, Prince John, back from the dead and walking around in drag -- which isn't likely at all, is it?.
There is no reason whatsoever to suppose any connection between Miss Bunting and Lady Rosamund.
Doubt she is related to the Granthams, but maybe we are waiting for another deus ex machina event, like the revelations of Charles Blake's future wealth and title. Perhaps she is in reality a great heiress (untitled) like Daisy Warwick was before she married a future earl, becoming the countess of Warwick, but was in fact a socialist all her life, eventually spending lots pf her money on "good causes", while living the high life, and dying relatively broke. She lived in the DA era, and is mentioned by Rosemund, as "stopping by the Warwicks" before coming to the Granthams party in Season 4, Christmas episode, dragging Sampson there, not taking "no for an answer"..