OK, so guys for the most part at my gym are pretty smart and DO NOT bother me during training. The way guys usually break the ice is by asking or saying "i heard you're competing in this" or "What are you training for" Which in reality is like a huge compliment so it always makes my day followed by loving to talk to this cute guy who is "interested" in what I'm doing with my training.
So like someone said earlier, definitely approach her with the whole competition thing AFTER her workout.....girls really like it. But if you notice she's one of those girls who kind of doesn't really smile at anyone cuz she likes to just train and keep to herself but she does so happen to smile at you...then most likely she digs you so go for it!!!