He doesn't say anything beyond that. He just waits for her answer and sees what happens after that. The girl either comes home with him or she doesn't.
I've seen websites that totally hype up this approach as if it's the ultimate, most powerful way to approach a girl for casual sex. But I don't agree, and I'll explain why.
It's not that this is a particularly bad approach per se. In fact, it is partly Direct, and I think it could work to get you laid from girls in nightclubs if you did it on enough girls with a confident attitude. Certainly it's better than 99% of the PUA material out there. And I do agree that keeping it blunt, short and to the point is the most effective way to get casual sex, especially in a nightclub.
However the first problem I have with this 'shock and awe' approach is that it's incomplete and a bit vague; the line 'do you want to come home with me' doesn't state specifically WHY you are inviting the girl back to your place. But with TRUE Direct, you must state your intentions to a girl.
You might think I'm splitting hairs here and that 'she'll just ASSUME you are inviting her back for sex', but that's not always the case. A woman could just assume you were inviting her there for some drinks and some friendly conversation, and when you start to 'make a move' on her out of the blue it could turn sour. This has happened to a lot of guys who aren't Direct about their intentions.
If a guy approaches a women with this approach, I think a lot of women would say 'Why?' after he says 'do you want to come home with me?'. Most guys, especially PUAs, would slip up at that point; they'd deny that they want to have sex with the girl and make some bullshit excuses such as 'we can have a few drinks' or 'chill out together' or some other lame excuse.
For me, if I was using this 'shock and awe' approach, I'd modify it by letting the girl know specifically WHY I am inviting her to my place (which would, of course, be to have sex with her that night) by saying something like 'I think you're really attractive. Do you want to come back to my place for some no strings casual sex?'.
The second problem I have with it is that the guys who came up with it act as if it's the boldest thing you could ever possibly say to a girl, as if they've thought of something massively controversial that takes huge balls to say and as if they've discovered the 'golden key' to getting women back to their place for casual sex.
Well, I'm going to be blunt, this shock and awe approach isn't actually all that shocking. Not to a hardcore Direct guy like me. In fact it's pretty tame compared to some of the things I say to women when I approach them. I often like to use erotic/sexual talk in my Direct approaches with women, and this works well for me. Compared with the Apocalypse opener, the things I say to women are MUCH more 'shocking' and 'controversial'.
The Apocalypse opener may seem shocking to PUA type guys because they are used to using weak, indirect conversation starters such as making a comment about the situation, asking directions or asking a girl's opinion on something, etc. So I can see why the PUA community might think 'wow, the Apocalypse opener is so bold and amazing, it must take massive balls to say something like that to a woman!'. But to a Direct guy it's not that amazing really, especially if he's mastered the art of using erotic/sexual talk in his approaches to get women turned on with his words and confidence.
The other thing I dislike about the Apocalypse opener is that it's taught as if it's a technique or tactic or canned line that must be remembered, something you can pull out of you 'bag of seduction trick's and use on women to magically get them back to your place. But TRUE Direct isn't a technique, tactic or a canned line; it's something more real and authentic than that.
If I was in a bar or club and saw a girl I'd like to get back to my place for sex, I'd start by letting her know I think she's attractive, then I'd say something like 'I'd like to take you back to my place and make passionate love to you. Are you interested?'. This is much clearer and more specific than the Apocalypse opener is.
Don't get carried away and fall for the hype around the Apocalypse opener.
And while we're on the subject, if you're interested in learning how to do ULTRA bold Direct approaches where you use erotic/sexual talk in your Direct approaches to get women turned on (without being creepy or freaking them out), I explain exactly how to do so, and include actual word for word examples, in my second ebook 'The Direct Approach Ebook 2: Taking Your Direct Approach To Mastery Level', which is available on the 'Products' page of this website.