You ask a woman to hang out, point blank. Movies, dinner, whatever it is.
Regardless of how interested they are, there is a 50/50 chance they will say "No" due to prior arrangements or their schedule.
Your premise is not quite right. If they're interested, there's a 100% chance that even if they have a crazy schedule, they're going to try and fit you in - IF they're interested. And that's what you want to figure out. But you have to set this up correctly:
When you ask a woman out, don't ask a few days ahead of time. You want to ask her about a week ahead because then the chances are less that she actually has something already planned or her schedule doesn't permit it, in which case, she's free to go out with you.
You want to gauge if she's really interested in you or not, so you can't muddle it up by starting off with asking for a date just a few days away that she's more likely to already have made plans for.
So, say you call her a week ahead or so and ask for a definite date and time. For example, you call Wednesday for the next Tuesday. If THEN she says, "Oh I'm gonna be busy", "I have tests", "I don't know what my schedule is for then", "My sister's coming in from traveling in Europe and I haven't seen her in ten years", then she's not interested. She's blowing you off. As opposed to three days away, lt's less likely that she actually has plans made already for a whole week away. Asking for a week away also makes you look like the busy, popular guy with a life.
But if after she says she's busy, in the next breath she counter offers with another definite time, i.e. she says, "Next Tuesday's not good... but Wednesday is!", then you're still in the running. She genuinely is busy, but she wants to see you. Like I said, she'll try to fit you in.
I also go with the practice that you don't ask them out for a Friday or Saturday night for a while so that 1. They start thinking you're a popular guy and not some lonely loser without plans for the weekend 2. They wonder why you only call to see them for a weekday night and 3. They'll ask YOU eventually, if they're interested, to take them out on a weekend night. You're making them chase you.
Don't you ask for another better time, nor offer one. You have to see if she does. That's the only way you can tell if she's interested or just blowing smoke.