In your first post, TB, you described the "embarrassment" of asking someone out for coffee. I know this feeling, and I have had this embarrassment many times. But guess what? It's a learned behavior. Maybe something happened to you as a child or young adult to set you on this path to where making a date request now seems as daunting as launching a mission to Mars.
The truth is that, since this is not a part of your DNA, and since this is behavior based upon a life lived in fear of asking women out on dates, the good news is that this negative behavior can be unlearned.
You may be familiar with Toastmasters. If not, it's an international organization primarily created to get people to overcome their stage fright when giving speeches, and also improve their general communication skills. If Toastmasters can cure people from the paralyzing fear of public speaking, then you can get over this obstacle of asking a woman out.
The first thing, I feel, that you need to do is link the comfortable feelings you have in normal conversation with women to the date request for coffee or tea. If you behaved the same way in both situations, you'd see that asking a woman out to have a coffee is no more than an extension of a friendly conversation and an friendly invitation request to continue it elsewhere.
But what stops you is the deep-seated memories of past incidents, the fears, the embarrassments that stopped you before, so you are currently locked in a cell that your brain made for you to protect you from harm. Unfortunately, your brain can be your own worst enemy, and it's time you overcame your own brain.
You need to practice, and you need to act as if you have no stake in the outcome.
This is important. For example, if I like a girl, but I over-think her to the point where the actual date request becomes a monumental task in my head, then the odds of my success are practically nil. However, if I am casual, and I float out the invite as if I were asking a bystander which way it is to the nearest Tube, then the outcome is almost irrelevant, and any answer will suffice. At this point, all you're looking for is information. Yes or no. But if you build up her answer in your head, the more emotion you will feel when she answers.
If the answer is no, you won't feel rejected, and you can say something like, "Okay. Well, when you change your mind, you know where to find me." But if she says "Yes," you have your date, you can dance a merry mental jig, and off you go.
The key in this is to practice the embarrassment out of you. Grab a friend and practice asking them out until it is no longer a big deal in your mind. Have your friend reject you every time, and devise various ways to respond with style and flair without telling her to "F-off." lol. If you don't have anyone available for this task, do it in the mirror. Feel the embarrassment with each attempt to ask her out. Also, imagine ways to recover from a "no" answer, and continue until the asking becomes nothing more than a comfortable and friendly gesture.
If you can act indifferent to the outcome of asking a woman on a date, you will be less likely to avoid asking her in the first place.
I hope this helps.