emilyr said:
There is a cycling club that organizes a beginning ride that leaves from Palermo 14:30, Av Libertador y Godoy Cruz every Saturday. There might be some blackout dates during the winter, I am not sure.
Great for folks like expats I would imagine who are new to the city and are still getting to know it and would love a tranqui ride where they can get to know other Argentine cyclers.
Ride on!
This is the kind of thing that I think you are talking about.
Also, I've seen serious cyclists around the northern parts of Recoleta and parts of Palermo along Av. Libertadores & Figueroa-Alcorta. They start off early on Saturdays I think and ride to Tigre (about 18 miles to the north).
Though there are more bike paths now, that's probably not what you're looking for.
And though Critical Mass might offer an opportunity to find other serious riders, a 5km ride at 3 to 5 miles per hour is not what your bike was made for.
If you can't actually find a cycling club online, but you Spanish is pretty good, I would seriously consider just riding around near the MALBA (museum) on Figueroa-Alcorta somewhat early on a Saturday or Sunday and then asking the groups you see if they know of a club.
Another thing to do with be to find higher end bike stores and ask the employees what they know. There is one on Scalabrini Ortiz between Santa Fe & Arenales (Palermo) that has some pretty nice bikes and those guys should know something.
Correction:
I just googled your bike and see that it's more of an off road bike. In this case, check bike stores and Critical Mass. The road cycling clubs might not be of much help.