If you are going to try to get a chick out that day, just simply say something along the lines of:
"I actually have a rare free (Monday) evening. I'm going to go to ________ place and grab a drink at 8. Why dont you join me"
That's it........does not show total availability and I get a good response from it. It works on chicks I just met as well as chicks in my rotation (who already know that I AM really that busy.)
Saturday morning I got a friend request from a chick on fb. She is maxed out at 5k friends so we had quite a few mutual friends. I sent her a quick message after accepting her friend request, chatted just a little. After a few messages I sent "I'm currently driving. Shoot me your number ". She did, I called her while driving. After 5 minutes of talking I said "I actually have a rare free evening tonight bc a friend of mine who I was supposed to meet up with has the flu. Why dont you get free and join me for a drink".
She told me that she had a bday party to attend at 5:30 that evening. I told her she could let me know if she wanted to meet afterwards, if not we could figure out another day once I figured out when I could get free again.
She told me she would let me know.
About an hour later I get a text from her "if you're still free this evening, when and where do you wan to go?"
Ended up being a pretty good date.
So its very possible.
There is always the chance of a chick backing out no matter if it's the same day or a week out.
Just shoot your shot, act cool either way and go forward based on her actions.