Re: What to say to invite a girl home?
In your situation I wouldn't have tried to take her home right away. I would have gone for a bounce. "I want to grab a slice of pizza with you. Come on."
From there, you're in a better position because a slice of pizza isn't as big of a commitment as going home to your place, it works to isolate her, and it increases her level of investment.
Once you get a girl to the point where she's willing to go home with you, a simple, "Let's get out of here," is all it takes.
As an aside, when I'm with a date at a bar, I really like the line above, "Let's go somewhere more comfortable where the drinks are less expensive." I've used this line a couple times.
"It's only after we've lost everything that we're free to do anything."