So there are a couple ways to translate this commentary. It’s more vague in Japanese than English.
The most direct translation is more like “Can we go home together?” The problem is that in English, this sounds a lot like “Can you come over to my house?” However, the phrase can mean simply leaving work at the same time, taking the same trains, traveling together until they must take alternate routes to their houses. I think “leaving work together” conveys this timid request better. She’s making a very simple request and it’s taking every bit of her courage!
That said, you could take it as something more, especially if you’re an overtly hopeful person AKA basically anyone begging Douki-chan to hurry up and put that red lingerie to use!!! (Some of the Twitter comments certainly took it this way.) So I’m a little hesitant to use this slightly-less-than-literal translation, since it conveys the hopeful interpretation slightly less well.
Translation’s tough. I never realized how difficult translating even “simple” one-line sentences can be. You’re always compromising on something.
