Unfortunately, there really isn't. Her only option would be to either visit you on a visitor visa every so often (though 6 months at a time, every year is risky as it might look like she's trying to use it to live in the UK without a proper visa), unless she can qualify for another visa, but even then, the only options would be work visa or student visa.
While there is an Elderly Dependant Relative visa, the rules are so strict for it that it's almost impossible to qualify for and very few are ever granted.
In order for her to qualify for it, you would have to prove that:
a) She is completely financially dependant on you and has no money of her own
AND
b) She is completely physically dependant on you and needs you to care for her and help her with every day tasks such as eating, dressing, moving around etc.
AND
c) She has no living relatives in the US who can care for her and she has no means of getting the care she needs in the US.
Basically you have to prove that she has no choice but to live with you, because she won't survive if she stays in the US.
