Understand that being that this is a quiet person, they may be relatively uncomfortable with conversation at first.
Thereby, you shouldn’t begin to worry if you have approached this quiet person and you are attempting to start a conversation and they don’t seem to be as talkative initially.
It does take some time before a quiet person would be able or willing to talk more and allow themselves to get into the conversation on a deeper level.
The girl may not have brought up the fact that she had a boyfriend because she may have truly believed that it was just conversation that she was having with this guy.
Some girls are not always thinking about a guy’s ulterior motive in talking to them.
Most girls who are interested in you as the guy would prefer that you ask for her number instead of give her your number first.
When you ask the typical girl for her number, she feels like you may be interested.
If you ultimately use that number to call or text her and start the process of getting to know her or ask her out on a date, she becomes more and more certain that you are being serious.
Try not to think too hard about the approach or the woman in question. 
Yes. 
Understand that being that this is a quiet person, they may be relatively uncomfortable with conversation at first. 
You are using the word, “most likely.”
Most guys would feel flattered if the 
Most people would be 
The girl may not have brought up the fact that 
If you are mentally ready and 
You are too stuck on the end result.