First of all...
Most people who ask this question (including myself a while back) were actually asking for a different reason. It's not that they don't understand the mechanics of how to ask a girl home. It's that they feel that it's "creepy" or "weird". They usually hope that someone will give them a magic line which all of us sudden sounds "not creepy". Personally, I was terrified of inviting girls back home because I had this feeling that the girl would respond by look at me like I'm retarded. Or saying something like "umm...what did you say?". Or by getting angry or disgusted. Or judging me or being scared off because I tried to move too fast. If you can relate to this in any way, your question is actually something different. It's "why do I feel like propositioning sex to girls is creepy?" or "how do I get rid of sexual shame?"
To answer your question...
This is a very overthought and over complicated concept in the pickup community. The truth is, if you invite a girl back to your place, she always knows what your real intentions are. So it really doesn't matter how you ask her. Therefore, the excuse could be literally ANYTHING. Introduce her to your dog. Watch a movie. Play a board game. Cook dinner. My personal favorite is to drink alcohol or to just ask her if she "wants to hang out at my place" (I don't include a reason or activity). Why? Because that's very blunt. If I'm asking her to drink with me or "hang out", that's almost the same as asking her if she's dtf. I'm being honest and letting her know exactly what I want. Contrary to what I used to think, this actually puts her at ease because now she can make an informed decision and she knows I don't have a hidden agenda. Hell...Hector (one of the writers) likes to throw away excuses altogether and directly ask them if they want to fuck. And it works great for him.
