How do you know when you have reached your body's vo2 max potential?

Btw, this covers a couple areas in this forum, thus decided to post here. Plus, I tried advanced search with my thread title and struck out. If you recall an old awesome thread, please share the link.

OK... here is the crux of it. I am training for my first century. Went out on a training ride w/a strong cycling guy buddy today. Route w/a climb that was the steepest / toughest I have ever personally done.

He kicked my butt on the climbs. I expected that for serveral reasons... one of which, he's a guy. Google reading I found that men typically have a higher vo2 by 40-60% over women.

Also in reading, I found that a person can improve their vo2 max w/training... BUT, only to a certain point.

I think I'm already pretty fit in other ways I could improve myself. I assume my asthma would be a medical disadvantage--though it's in pretty good control w/meds (my doc knows I'm a cyclists, btw).

Hmmm... I am going to closely watch my HR stats in my Garmin TC on this particular climb over time as test.

Will more training actually make me more fit? Or am I already there?

What's reasonable to notice a change in terms of a time table w/training etc.?

Oh... I do know you can get a lab test... never had that... not sure where or cost... if you've had one and can add anything in relation to what I ask, thx too.

TYIA
Miranda