You have a resource that perhaps you don't recognize, your dance partner who confirmed that a girl was giving you the eye. Can you ask her for a female opinion? I'm not trying to complicate your life, but did your female friend ask you to join her at class because she herself has some feelings for you?
Feeling feelings may be new, even scary, but it's not fatal. Go ahead and ask the woman you like to join you in some low-key activity, like coffee, etc. If she turns you down, knowing where you stand with her is better than wondering. If she accepts, maybe you'll enjoy the time together. Intimacy and being close are still some ways down the road after coffee, so try not to get too worked up about that.
"Telemachos, your guest is no discredit to you. I wasted no time in stringing the bow, and I did not miss the mark. My strength is yet unbroken…"—The Odyssey, translated by W.H.D. Rouse