She takes hours to text back but said yes to date

A reply that takes four hours is normal for a lot of people, especially when they're working, looking after someone, or simply not on their phone. What tells you more is how the thread behaves when she does write. If her replies are warm, she asks something back, and she's the one suggesting times, the delay is probably logistics. If her messages get shorter, she stops asking questions, and she only answers what you asked, that's a different signal.

Look at the whole pattern across a few days, not one exchange. One slow reply on a busy day tells you almost nothing. Three slow replies where she still follows up with a question tells you she's engaged but stretched thin. Keep that in mind before you decide the date is at risk.

You also already have the strongest evidence you're going to get. She said yes to a specific date. People who are losing interest rarely commit to something concrete.

When someone is juggling a lot, the texts that get answered are the ones that ask for one thing. Name the day, the place, and the time, and end with a question she can answer with a word. Something like asking whether Thursday at seven still works, with the wine bar named, gives her a clear yes or no. Anything that needs her to think about her week, or to reply to three separate points, is likely to sit unread until she has a spare minute.

Keep the logistics in your own hands. If she's going to be late getting to a reply, make it easy for her to say yes to a fixed plan rather than to propose one from scratch. Suggest the place and the time, leave her room to change it, and don't open the thread with a list of questions about her availability.

A reasonable window to wait before following up on a slow reply is somewhere around a day, longer if she told you she had a heavy week. Sending a second text within an hour of her last one reads as impatience even when you don't mean it that way. If you do need to check in, do it once, in the late morning or early afternoon when she's most likely between things, and keep it to a single line about the plan.

If you've checked in once and there's still nothing, let it sit. Give it another day or two. If she still hasn't replied, or she replies with something vague that doesn't commit to a time, the most useful thing you can do is stop chasing and let her come back to you. If she doesn't, you've learned the date wasn't going to happen with her, and you can move on without having spent a week on it.