OK. This all sounds normal and familiar. There were many times in the past where I felt that a girl liked me, and yet I had no courage to say anything. One of the main things that helped me was an acceptance of my own awkwardness. When you dropped the box of laundry tablets on the floor (something that most of us are likely to do, especially since Asperger's is often paired with proprioception deficiencies), you have to learn to own it. Giggle with her, verbally acknowledge your clumsiness, and laugh about it ( a bit of a self-deprecating sense of humor is required).
You couldn't pull it off the first time you tried. It doesn't mean you can't try again. The main thing that I've learned: it WILL NOT play out like whatever scenario you thought of in your head. We tend to overthink things, and unfortunately this prevents us from taking action. You can imagine the scenario where you ask her out, but you cannot commit to it. The actual scenario will not take place and you will not be able to move forward if you get stuck on the thought "This isn't what I imagined."
You say that you both have conversations. Forget the plans, forget conveniently forgetting something to go buy again, and forget trying to place the ball in her court by leaving your contact information. The next time you two are conversing, take note that you are having a conversation. Work up some courage, and during the conversation simply ask "Would you like to go out with me sometime?" Trust me! It is something that must be done so that it can be done again in the future.