Phoning her for a date?

Alright, short bit of background. I'm heading to uni in September, so is this girl. I have had feelings for her for a while but never got them out and actually asked her out and even though we'll be far away from each other in a couple months I wanna ask her out, whether it's a one-time thing and a good memory or if it leads into an LDR (which I'm not sure if I want, but I want her and I wish I was further on in life).

I have her on FB and Insta but don't actually have her number. In an ideal world I'd meet her in person to ask her but that's not really possible anymore given we've left college, or I'd ring her up but my house is small and I'm never home alone so I'd have to broadcast everything to everyone, I could go out but need an excuse. Or I could just message her and ask her for a drink some time before uni cause I regret not asking her out. What do ya think I should do? Message seems a little cowardly but if she accepts and I'm confident on the date it doesn't matter right?

It's unlikely to work but as long as you're willing to do it without expectation of anything then you could try it. But don't put much effort/stress/hope/feelings into it because like I said the most likely outcome is that she will be shocked and say no.