What is there to do when a chick approaches ME? It usually catches me way off guard, which causes me to hesitate, or overreact, ultimately losing my cool of the situation. Any ideas/thoughts?

Well, you're doing good! You probably have something about you that attracks her.
To your question, in my humble opinion, you're attached to the outcome of the interaction, you've got some inner game to do! As long as YOU care about what SHE has to say, then she has POWER over you. Because a girl approaching is always a kind of unexpected she will normally be leading, you've got to flip the script. In such a situation I would apply some cocky/funny lines of funny conversation, like:

(just before she starts talking) Hey, two martini and one beer please (or something)?
She: I'm not a waitress!
You: I know, but if you get them ... then you will earn the right to talk with me, *blink/sly smile

Or (credits partly to David dA if i remember correctly):

She: hey, my name is blabla
You: you want to buy drugs?
She: No, why?
You: Cause I talked to three people last night who wanted to buy drugs from me. (a bit of storytelling here).
She: really / no way
You: you know what, you can be my favorite junk from now on, let's sell some drugs!

Take her by the arm and leave. Then you can talk about other people from whom you expect they would use drugs etc.. Just flip the script and have a fun and open attitude!

Everyone is different so you have to try what fits you personally, hopefully my post helped a bit