Checking into your local general aquarium society is a good start. You can drop off flyers announcing the creation of a betta club (just be sure to have a website/facebook group or something ready to go).
You might need to expand your search beyond what you consider to be "local". You east coasters are all squished in there together, but here in California its pretty normal to drive an hour or so to get to a fish club meeting. For CBS, we have members that drive several hours to our shows. And CBS members travel 6+ hours down to southern CA to help with the Golden State Betta shows. The internet brings us all closer, so the distance isn't as big a deal anymore. In person meetings are awesome, but not totally necessary until you start thinking about having a show, or doing a group buy on Aquabid, or something fun like that.
IBC Executive Board Member-at-large, IBC Judging Board Liaison & Registrar, IBC Certified Judge
Member of the California Betta Society
Aquabid user: Bulldogbettas