She keeps saying she's busy when you ask to meet

One "I'm busy" tells you almost nothing. Three or four in a row, each one paired with continued texting, tells you something specific: she likes the conversation but hasn't decided the in-person version is worth the effort yet. Look at what she does with the texting itself. Does she ask you questions, pick up threads you dropped, send things unprompted? If yes, the interest is real and she's probably just uncertain about meeting or about the timing. If her replies are short, slow, and only answer what you asked, the texting may be a low-cost habit for her rather than a sign of building momentum.

Also check whether the busy weeks are real. Some people have a packed job or a family situation, and you'll see it in what they mention about their days. If she describes her week in detail and it sounds full, take her at her word and move the ask to a specific later slot. If her week sounds open and she still defers, that's the more useful signal.

Vague plans keep dying because they cost her a decision every time. "Maybe sometime" lets her skip the decision entirely. A specific time and place with a short window forces a yes or no, and a no is far more useful to you than an endless maybe. Pick a day, a time range, and a place close to where she is or on a route she already takes. Keep it to an hour or so so the commitment feels light. Offer one option, not three, because choice pushes people back into thinking.

Also make the ask feel like a continuation of what you're already doing, not a big leap. Refer to something you talked about in the thread so the meeting reads as the next natural step and not a new formal request. This lowers the stakes of saying yes without you having to lower your standards or water down the invitation.

After one clear ask and one deflection, let the next move be hers. You can keep texting about her day, your day, and whatever you were already enjoying, but don't re-pitch the date in every message. Repeating it within a day or two reads as pressure and makes her busy excuse feel more justified. Give it a few days of normal conversation, then, if she hasn't offered anything, make one more concrete ask with a new specific option. If that also gets deflected, you have your answer, and continuing to build on a conversation that never leads anywhere will cost you more than it gives back.