That sounds frightening to someone with social anxiety...
Yeah, that would be the last time I show up to that gym. I'd feel it was my fault. and that I was bothering them.
You bother people every day with your existence. You are one more car in their traffic, 5 minutes more of waiting in their line, you got the last bagel they were craving. Being a bother to people is part of living in a society, it would be impossible to live without ever being a burden or a nuisance to anyone. I wished I had accepted this earlier in life.
The important thing is to realize that this feeling is irrational. People aren't strongly bothered that easily. Quite the contrary, extroverted people tend to be much more popular than average.
"Korean girl Short I didn't know how to start a conversation with her, so I just asked if she was Korean and she said yes. Then I made her guess what kind of Asian I am. Then I rambled about being Asian in Syracuse before leaving. I initiated one more conversation but now we don't interact"
So endearing!