Do girls hover around a guy they like trying to get noticed?

There is a girl I've known for about 6 months that I see around my crossfit gym. We always flirt and have a lot of chemistry, I plan on asking her out next time.

Anyways, just wondering something i've observed. When I show up she'll seem to hover around me (within a few feet) pretending not to notice me or say hi. If I approach her, she becomes flirty again with playful touching, jokes, etc.

Wondering if girls will hover around a guy they like pretending not to notice, but wanting me to initiate?
Do girls hover around a guy they like trying to get noticed?
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