Trying to work out why she uses the words she uses is a rather pointless exercise. If she was really interested, she would say something along the lines of "I'm busy that day, but how about..." and she offer an alternative.
If I were you, I'd just occasionally invite her along to things you were already going to. If she's too busy, it's no biggy - it's something you were going to whether or not she accepted your invite. If she declines too many times, move on.