You want a line, fine. I'll give you something you can use, but it has to be qualified a bit, basically by repeating what kowalski told you.

People focus way too much on openers and hypothetical lines - it's like obsessing about a single line in a conversation is like obsessing about toe position in the wind up in baseball. Then when push comes to shove you go up with your amazing wind-up and it's a bunt with no follow-through.

2 general rules here I always found useful

1. You can't really predict a goddamn thing about how a given person will react to you
2. Talking to people is not a big deal. But the more you treat it like a big deal, the more they'll feel like it is too.

It's pretty unlikely she'll say "Why you speak to me after 4 months". That's your perspective because you've been thinking about it for 4 months. She almost definitely hasn't. Girls get guys talking to them all the time. She is much more likely to be wondering "why is this guy talking to me/hitting on me at the gym?".

So if you want to talk to this girl just be friendly and non-commital. Again, not a big deal. When you see her go:

"Hey, how's it going?"

If she's responsive and talks to you, then you can get out in front of your own imaginary shit test if you like by being like

"Cool, we've never spoken before have we? I'm {name}"

There. Simple. No pressure, won't make things seem weird or like a big deal. From then on you can chat to her when you see her around.

Honestly though, if you're not gonna do this in a friendly kind of way like that, if you want to make this a big deal where you're "approaching" or whatever, best to leave it really. If you go into this expecting to make something happen or "work" right away you'll just make it uncomfortable for the both of you. Which isn't great if you both want to work out there.

Again, just repeating what kowalski said (because it's what we've all ben saying to new people for forever), go out and get some experience talking to girls in a more appropriate setting. If you're obsessing about one line for one girl you happen to see in the gym, chances are you'll need more experience to be able to get out of your own way - and there are better settings for you and other people than the gym to do that in.