From personal experience though years ago, when I was at the gym to work out, I usually had another schedule I was trying to fit it into so I needed to focus on my exercise which didnt have ANY TIME to socialize. I would acknowledge someone I interfaced with for whatever reason it related to me exercising but nothing beyond that.

Honestly I did my most gym socalizing playing racquetball with the guys. I especially enjoyed the challenge court because while waiting for my turn for the challenge I could socialize with the others who were waiting too. Have to admit not many women were up to the top players that played the challenge court..i was the only one at times but thats when I got to meet other guys to set up games with also. Not much socializing on the court but there was more connection made given the competition & the acknowledging good shots. Enjoyed the racquetball interface much more than exercising which is individual & FOCUSED.

I wouldnt push anything with women. Simple little connections great. If you run into someone on their way out & can struke up a conversation on the way checking out or heading out to the car, that would be much more relaxed & better accepted unless they are in a hurry...be sensitive to the person you talj with