yes. . . say hi, introduce yourself. . . Maybe try to start a conversation on whatever training she's doing, since you know you have working out in common? If you get talking for a few minutes and it seems reasonably comfortable and natural, you could ask if she wants to be workout buddies. . . tell her she's so pretty that it'd be great motivation for you to show up. If you wait till you're sure she's comfortable with you to say that, it will almost certainly make her happy, even if she says no.
Good luck. 
_________________
And if I die before I learn to speak
will money pay for all the days I lived awake but half asleep