The girl cannot settle in the UK as:
a descendant -- her parents were not born in the UK
a spouse -- she's not married to a UK citizen
a fiancee' -- she's not engaged to a UK citizen
an au pair or working holiday-maker -- she's not a Commonwealth citizen
a domestic worker -- she has not been employed by you in a domestic capacity in the US
a singer -- she will need a work permit and as I suspect that a) she's not a professional singer and b) you can't prove that there's no one else in the UK or EU who could sing for you
an artist or composer -- again, I suspect she's not a professional
a tourist -- she can visit, but must leave within 6 months. she may not be granted leave to enter for 6 months if it appears that she cannot support herself here or does not have strong ties to the US
If she will be attending university in the fall, she can come over after completing one semester on the BUNAC program, which will allow her to live and work here for 6 months.
She can also attend university in the UK, though, as I said in your other post, the cost may be prohibitive for an international student.
If she's not planning on going to university or her parents weren't born in the UK or somewhere in the EEA, her options are extremely limited.