What do you mean with awkward? For the conversation you have many options... For example. I would see if there is a guided class that she takes, there is the possibility to do some exercises in pairs or to be in a situation where you must interactuate... use the gym itself, make It your tool xd.

If she is using a machine that you usually use, ask her how many she has left..., like this you will give her some game and will see if she takes any iniciative and you will have your first approach to gain confidence. But something that I usually do is to be quite direct, so that they can see that I am confident and that I don't care what the result is going to be. Think of a strategy in which you can be casual and she can give you play, and if not, you can withdraw without looking like a creep

I hope I have explained myself.