OMG, Candis!! Thank you SO much for having such a clear memory of the Women's City Club!!!
Their "bobbing" requirement you described was EXACTLY what turned me off of swimming forever. The large female teacher got very frustrated because I couldn't get it, so she grabbed my head and started forcing it in and out of the water! Naturally, I was choking and gasping, and being a tiny little girl had no way of fighting off this (to me) giant lady.
I don't recall any more "lessons" there, and I suspect this is why my folks later forced me (when I was around 12) to take lessons at Larson - hoping a second time around would take. Little did they know that at the first lesson we were supposed to just jump into the deep end and immediately head to the side. I balked. Every Saturday after that (for 6 weeks), I would dutifully walk down 19th Ave., and then veer off onto Taraval - and spend the hour reading books at the library. I'd then go to the gas station, wet down my suit and dampen my towel in the bathroom sink, and head back home. My parents never found out!