I asked my friend out on a date. 2 times she rejected me. In January, She questioned whether to talk to me anymore so I left her alone for 2 months. I just began talking to her again but I keep it short n simple only speak when I see her at work. I don't text her anymore. If I look her way she smiles and looks away. I haven't asked her best friend what she truly wants because I don't wanna put her in the middle nor do I want to jump to any conclusions. What should I do?
Girls, Seeking advice on what I should do?

What Girls Said
The question is why do you want to ask her out? What is your ultimate intention with that girl?
If she rejected you once, then I believe that this should be an unequivocal message.
I suggest you keep it on a friendly coworker talk basis only and don't attempt to get more personal with her. If she is really interested in you, then she will do the first move but given your history, I have doubts that this will happen in the near future.
Furthermore, it is never a good idea to attempt something with a coworker because this can cause too many problems within the company and notably jealousy or even mobbing.
Give her the space she wants and let her do the talking if she feels like it.
She rejected you once already, take that as a hint and move on.