Trust me, you are overthinking this. Calling a girl and asking her out is NOT a big deal. While it can be a little more scary, it isn't much different than calling a guy friend and inviting him to hang out.
Stress the EVENT, not that it is a "date." In fact, don't even use the word "date." It has to be "hang out" or "get together" or "catch up" or something like that. "Hang out" is classic. Or use none of the above as I did below.
Example:
Mike: Hey how have you been?
HB: Pretty good.
<Brief fluff talk>
Mike: Anyway, the reason I'm calling is that there is this really cool bar and grill called XYZ. They have really good bands play there and awesome chicken wings.
Mike: I wanna get over there at some point soon. I was thinking Thursday night about 7ish. Wanna go?
I recommend that you call her instead of texting. It shows more b*lls. Now if you get voicemail, simply leave your meet up suggestion as a voicemail. If she's interested, you will hear back. Otherwise, she will ignore you or give you an excuse. Either way, it's not a problem. You aren't doing anything wrong.
But, if you really feel better just doing this by text, then fine, just text her. It isn't THAT critical. Just get it done.