So what the fuck happened?
+100 on just being humorous. Make sure she isn't wearing ear buds or is facing your direction and say, "Hey, since we seem to be running partners is it alright if I get your name, I'm ______. Make sure to do this as soon as possible once you see each other before you start doing the, "I'm pretending your not fucking following me every day" bit. This will fill your mind with stuff that will block your A game. Wondering if she's looking at you and making sure you don't look at her etc is all just pussy shit. It keeps your mind away from the close. BTW, the best way to make a girl think that you have better shit to do than to talk and text her all day is to really have better shit to do.
Now, don't mention the fact that she's following you anymore otherwise she might get shy and start blocking you out to hold up her disposition. If she was bold enough to make moves she obviously wouldn't follow you around halfway creepy for a month. Just say that you see her around here a lot and that it takes a pretty dedicated regiment and life to keep up with that. Tell her your schedule didn't used to allow it until you got that job working for ______.
Apply it: "Now I'm an engineer for Intel with a flexible schedule so It works out, what do you do for a living?". Bam.
Do NOT think about how odd it is that a white girl is hitting on an asian guy. This is guaranteed to fuck you up.
Do NOT have any type of expectation going into this conversation. Even wondering how you'll react if she doesn't like you is something you don't want on your mind. Clear your mind and just focus on one thing. Hey, I see you here! Tell me about yourself. Just get her talking don't worry about anything else such as if she likes your muscles or your tight Asian ass. If that shit is on your mind = fail.
DO keep your player face on. You don't want to just say hi and then that's it. Then you'll just be treadmill friends. If you fuck your opening up, then it will be obvious later that she is on your mind and you are struggling for an entry.
DO take advantage of any opportunity to get her phone number. Tell her you've lost your phone and ask her to call it.
Go hide it or leave it somewhere of course.
DO find out what she does before and/or after the gym. You may have something in common that is easy to take advantage of conversation wise.
If you come up short, plant a seed. Find out a little bit about her so that next time you can have prepared something to act on. Like, if she likes art, go fucking buy some artwork and put it in your house so you can talk to her about it then show it to her later haha.
Hope this helps my Asian brother.