She said she's busy that week.

Take the reason at face value and do not ask for another day on the spot. Reply once, warm and unbothered, say you will get back to her, and then actually go quiet for about a week before you propose one concrete plan. If she offered another time herself, take it.

You suggested a day. She said she is busy that week. She did not offer another one, and that is the part worth noticing: a real scheduling problem usually arrives with a counter-proposal attached to it.

The move

What to send

Send this

No worries, my week's packed too. I'll hit you up next week.

What it means

What she's actually doing

Sometimes it is true. Sometimes it is the kindest available way to say no. You cannot tell which from the message, and trying to find out puts you in the position of asking for another chance. So do not sort it. Answer in a way that works for both readings: take the reason at face value, keep the next step yours rather than hers, and go quiet for a while. If it was true, nothing is lost. If it was not, you have spared yourself the version where you chase.

Timing

How long you have

Right after she says it
Answer in the same exchange, briefly, and do not attach a new request to it. The reply has two jobs: accept the reason without inspecting it, and make it clear the next step is yours. Anything longer than two short sentences starts to read as if you are still processing the news.
The quiet week
This is the part that does the work, and it only works if you actually do it. No check-ins, no memes to stay on her radar, no "how's the busy week going?". If she writes to you first, answer warmly and normally. The quiet is not a punishment. It is you having your own week, which is exactly what your reply said you would do.
About a week later
Come back once, as you said you would, with one concrete plan: a day, a place, something specific enough to say yes or no to. Do not mention the busy week or ask whether things have calmed down. You are not reopening the old invitation. You are making a new one.
If she is busy again
Busy twice with no other time offered is an answer, even if it was never said out loud. Take it gracefully in one line and stop proposing. If she comes back and is clearly in it, you lead again, and the date is still yours to propose.

Before you send it

When this backfires

Low, as long as you actually do the going quiet. Saying you will be in touch and then writing the next day is worse than never having said it.

Not these

Four texts that end it

  • Don't send

    Oh okay, no problem. What about next week then?

    Instant and eager. It answers "I'm busy" with another request, which says the week was the only obstacle and you have nothing else on.

  • Don't send

    Alright, let me know when you're free.

    It hands her the next move and then waits for it. If the busy was a soft no, this is where it quietly becomes a permanent one.

  • Don't send

    Are you sure? I was really looking forward to it.

    It asks her to manage your disappointment. Whatever she felt before this message, she now has a reason not to answer it.

  • Don't send

    Busy with what?

    It asks her to justify her own week to someone she has not met yet. Whatever the answer, you have made her explain herself, and the easiest way out of explaining is not answering at all.

After you send it

What her reply tells you

She offers another day herself
That was a real scheduling problem, and she has just solved it for you. Take the day she offered, or one close to it, and settle the place and time in one message. You do not need the quiet week now. That is for when she gave you nothing to work with.
A friendly reply, but no new day
Normal, and the reason the quiet week exists. Leave the thread there. Answer anything she sends in the meantime, keep it light, and come back with a concrete plan when you said you would.
She keeps texting through the busy week
She is too busy for a date, not for you, which is a good sign. Enjoy the conversation without letting it become the relationship. Keep it short, and use the warmth to make your plan easier to say yes to when the week is up.
Nothing
Your message did not need an answer, so silence here is not a no yet. Do the week anyway. If the concrete plan you send after it also gets nothing, that is the answer, and you let it go in one short line or not at all.

Also asked

Questions around this one

What do I say when she says she is busy this week?
Accept the reason, do not ask for a new day in the same breath, and say you will get back to her. Then do what you said: go quiet, and come back about a week later with one concrete plan.
Is "I'm busy" a soft no?
Sometimes. The tell is whether another time comes with it. A real scheduling problem usually arrives with a counter-offer, while a busy with nothing attached is often a polite no. Answering both the same way is what spares you the guessing.
How do I not seem needy when she says she's busy?
Do not ask about next week, do not say you were looking forward to it, and do not check in during her busy week. One warm, short reply and a week of your own life does more than any line could.
Should I ask her which days she is free?
No. That hands her the calendar and the decision. You lead the logistics: when you come back, propose a specific day and a place she can accept or decline.
How long should I wait before asking her out again?
About a week, or whatever your reply promised. Sooner reads as if the week was the only thing between you. Much later and the thread has cooled enough that your plan has to restart the conversation too.
What if she says she's busy every time?
Busy twice with no new time is an answer. Take it gracefully in one short line and stop proposing. If she comes back and is clearly interested, you lead again with a concrete plan.

One line, written for your conversation

The text above works because of what it does, not because of the words. Screenshot the thread and Valerius reads what she actually said, where it stands, and writes the next message in your voice.

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