How to respond if she says she already has plans for that day?

A line like 'I already have plans that day' is one of the most ordinary things a person says while they are still interested. She has a calendar, she has friends, she is not sitting at home waiting for your text. If you read it as a rejection of you, your reply will carry that feeling, and she will pick it up. What you want her to see is that you heard the Saturday part and that the rest of the conversation is still on.

Look at what she actually offered. She did not say she is busy for the whole week or that she is not interested. She gave you a specific day that is taken. That is information you can use. It tells you the timing was the issue, not the invitation, which means the next version of the invitation can simply move the date.

The shape that works here is brief acknowledgement, a light signal that you still want to meet, and one open day or window for her to pick from. Acknowledgement means you take the plans at face value and do not ask about them. The signal means something plain, like saying you would still like to get a drink, so it is clear the invite stands. The open day means you name a time that is actually free for you, so she does not have to come up with a counter from scratch.

A draft that is doing this job is short and contains no question about the original plans. It also does not apologise for asking or explain why you asked. If your reply needs more than a few lines to land, it is probably trying to do a different job, like reassuring yourself. Cut it down until it only accepts, signals, and offers one option.

After you have sent the reply, leave it alone. If she answers with a new day or a time, match it and confirm the plan in one line. If she does not reply at all, give it a day or two before you do anything else. Silence after a scheduling message is normal, especially on weekends, and a second message sent the same evening reads as pressure. One gentle follow up later in the week, on a different day entirely, is fair. Something like suggesting the following Thursday as an option is enough.

Stop when you have made two honest offers on different days and she has not picked either. At that point the simplest read is that she is not planning to see you for now, and you can leave the thread open without chasing it. Being relaxed about that is what keeps you from looking like you only wanted the date.