Yeah, it's perfectly fine to do so. There's no way to apologize wrong. Well that's not true. If ALL you do is just apologize via text then yeah you need some home training. But it's a good place to start if you feel the need to do so.
You all had an awkward date. And then you ignored him in public. Ouch. You're going to need to follow that text up with a phone call. His feelings are probably a little hurt but most guys don't expect to speak to you again after an awkward date if both people acknowledge it was that way.
I do wonder what you're sorry about though. Date sucked. Okay, you moved on. See him out. Whoopty.
The last interaction you had was not a good one. It's wholly plausible to not speak to somebody again for which the initial interaction sucked. In fact, I think that's how most people would carry it. Do you want another date? Or the chance to maybe undo the damage from the first date. Sounds to me like you would have had an awkward hello to go with that awkward and uncomfortable date you just went on.
I don't know. Just realize that saying sorry might also be opening back up the doors of communication. If that's what you want, great. If not, you might just want to keep it moving and do a couple of Hail Mary's or something.
It was written.
apologize