I just texted my sister and asked her if she was free this evening. The reply was "no time". How should I reply? ..

First of all, you shouldn't ask her if she has time, which seems insincere. Just tell me what you want to do. You wanted to ask her out, but you didn't tell me directly. Girls can't see your sincerity, of course they will say they don't have time.

Secondly, there is no need to go back. According to your plan, arrange what time, call her directly before that time, and then pick her up.

Finally, take action, not just text messages.

Good luck!