The scene where Georgiana asks Bess if she'd be willing to leave despite the Duke asking her to stay made my blood boil. Her bold attitude in telling her no that she wouldn't leave? What a bitch! You are screwing another woman's husband and then you have the unmitigated gall to tell that woman that you won't leave her house?! Unbelievable.
I'm here to kick ass and chew gum and I'm all out of gum!
Well I don't think (in the movie anyway) Bess loved William at all, she only slept with him so that she could get her children back, and I'm sure she realized that refusing to remain his mistress would likely lose the support she needed to keep them. Georgiana probably realized that, but she just thought she'd test the subject one more time. I doubt that she really expected her to say yes.
Still, I think Bess quite proved her loyalty to Georgiana later in the film, and the Duke could have easily tossed her out for accompanying G to give birth to Eliza.
http://25.media.tumblr.com/tumblr_lpydj8CqLx1qazkdco1_500.gif