Your friend could have “hooked up” in a bar, the library, a coffee shop, or walking his dog.
Do you know for sure what happened next? I mean, did he come brag about his conquest, or could they have just danced for a while and then gone to IHOP for coffee and pancakes to get to know each other? From what you wrote, I don’t know that anybody committed any kind of sin. If a guy is going to get married some day, he has to do something to meet girls.
Even if they did (insert euphemism here), that was his choice, the choice of both of them I’d expect, but not yours.
Give yourself a break. Unless you said to your friends, “Hey, let’s go find some chicks (or whatever folks in Australia call girls) and maybe we’ll get lucky,” your pal and his new friend are responsible for whatever may or may not have happened.
Maybe you can find some other place to dance, like take ballroom classes or…I don’t know where else you could go to dance without bringing your own partner. Try line dancing, no partner needed and there may be clubs (groups of people type of club, not nightclub) there like we have around here that actually focus on the dancing part. It’s a family activity with married and single people, old people, groups of women married to non-dancing men, even children were in the group I attended.
But you didn’t do anything wrong.