If you're not going to call him - and it really is as simple as SingleMan has made it - you're going to have to wait until you encounter him again at some future event, by which time a more enterprising woman may have snatched him from under your nose, so to speak.
I've asked men out usually after I've got to know them slightly through being at the same events/parties etc - just a casual 'would you like to come to see...' or 'would you be my plus1 on...'. If they want to read into my invitation more than I've intended, that's their problem and if they say no that's their problem too. Offhand, I can't remember any who declined but there must have been some who got away from my evil clutches.
However, there was an occasion when I was introduced in passing to a divine looking guy by a friend - one of those situations where you stand on the sidelines like a spare part while the 2 of them have an intense chat about people they know, and you don't, before going separate ways.
Friend told me he was single and available, gave me his number, and a week or so later I called him. After telling him my credentials (friend of x, we were introduced briefly, etc), I asked him if he'd like to accompany me to a night at the opera (yes, I had tickets).
Much to my (very temporary) chagrin he said no (silly man), but when I bumped into him a month or so later and reminded him I'd called him, he invited me out straightaway. It transpired that when I rang him he couldn't 'place' me and was scared he'd be in for a evening of ... well, let's not go there.
Nothing ventured, nothing gained - and in these situation the spoils inevitably go to the fleet of foot.
As for texting when drunk - it's never a good idea to try and break the ice with strangers when you're paralytic/off your trolley unless you're certain they're equally loaded when you press 'send message'.