I know that feeling anywhere. Tyler from RSD refers to this fear "self-Hypnotics", people don't like to be hypnotised or even feel it but you are your best hypnotiser, it's true. An example of this is when you're in a loud club and you don't feel as though you can approach because you don't feel you will get any success, that's your brain hypnotising yourself. Any emotion you feel is self-inflicted but now that you know about this you can combat this by being consciously aware of what is happening and you can then stop it.
Your ego is the only thing getting in the way of any approach simply because it does not want to be hurt but you need to fix that mentality and like the feeling of getting hurt because like the old saying you will hear on this forums "Everytime you don't approach you have failed". Make approaching fun as though it's a new but old challenge, just get into the fun of it all.
Now time for the practical part of this: When dealing with a daytime approach I keep it stupidly simple and honest. The honest part directly translates to being direct with the approach. I go up with a simple "Hey, I literally just noticed you as I was walking out but I have to say this, you are literally the most beautiful (or cute, think of a variation) girl I have seen all day and all I wanted to do was come up to you and just talk to you." You can just transition to asking her name and engaging in some Fluff talk mixed with some flirting.
If it's a busy situation then a simple "Hey I know it's extremely busy in here and you look like you want to just run away from this madness and I can't blame you because I feel the same way (if you get a laugh here then the green light is up but don't take this dogmatically) but I just want to say that you're absolutely gorgeous and I just wanted to talk to you".
As for the Number Close, again, I keep it ridiculously simple and as for the situation you are dealing with something like "I know it's extremely busy in here but I really want to see you again just to get to know you better" then you can just get her number. Or as an alternative if you have a common interest of any kind such as cooking or music or even smoking weed (a personal one there) lol then you can make plans centered around that. For example "You know what, you have got to show me your cooking skills, lets meet up at some point and cook dinner together, what's your number?"
The key factor here is to deliver with a lot of confidence, even if you do stutter, just carry on. Think of the whole thing as no big deal and set that frame. Some may argue that this seems too direct or desperate but if it's delivered with a lot of confidence and eye contact then you really don't have to worry about anything. You can have all the lines or techniques that you want but if you don't believe what you're saying then you're not going to get anywhere. This is coming from a man who was a Mystery Method practitioner for many months and I didn't believe in Direct Game especially for my appearance but I see going direct as the way forward as you don't waste time to only get a same or worse results than I would with an indirect game but I still use direct according to the situation.
I am only responsible for what I say, not what you understand - The proverb of a true activist.
I'm not driven by fear, I'm driven by Danger