Everything you said after the bolded bit is your own bias, as you noted at the very end there.
It's only a big deal if you make it a big deal.
Lemme preface my advice by stating that a significant number of my lays were women I met out at a bar or club, or women I was out on a date with (usually from the bar, club, or a dating app). Point being, in most situations, it is late at night, on a weekend, and alcohol is involved, making it a much more natural segue.
Sometimes it'll just flow naturally. The chemistry's there, so I'll go for a kiss; she'll be receptive, so I'll ask her if she's ready to leave and wants to come to mine/go to hers.
Sometimes it requires some plausible deniability. Like when I was watching over my buddy's place in Philly, I suggested she come over to "meet the pets", on account of the cat, dog, and 2 ferrets.
And other times you just have to facilitate the logistics because she might not be a fan of PDA (public displays of affection). The girl I met at Seacrets this past weekend was like that, remarking that she isn't a huge fan of kissing in public, to which I suggested we go somewhere more private and invited her back to mine. Unfortunately, that didn't go as planned, but you can read about that in an earlier reply I left in this thread.
My advice would be to simply not make it a big deal. If you don't ask, the answer is always "no". Never explicitly state that you're inviting her/going to hers for sex. And keep moving things along unless you're stopped.