Cheapest way to get a return travel from Sheffield, Engalnd to San Antonio, USA and stay there for the Summer?

I really want to see my girlfriend in the US this Summer 3 problems are price, being able to raise very little cash and also that I have to stay in a hotel cos my girlfriend's Mum has never met me before.

What is the cheapest way to get to San Antonio, USA from Sheffield, UK?

tram, train, then swim!!!!!