If you can find any organized shooting events in your area, competitive or not, you have a pool of potential recruits.
Maybe some of the older ones are tired of competition and tactical equipment races, and are ready to relax and have fun.
Maybe some bullseye or Appleseed shooters are ready for something different.
Maybe just handling a lever action rifle and single action revolver at a gunshow would inspire some to visit.
I agree with showing up at a gunshow in full costume, but it might not hurt to also have someone wearing minimal age category clothing, such as jeans & workshirt, leather shoes & straw hat, in order to avoid scaring away those who are not (yet) interested in costumes and re-enacting. I believe some newbies are scared off by the expensive costumes they think are required.
If Boy Scouts need a place to earn their marksmanship merit badges, perhaps your range might be available on some summer weekday, and with plenty of .22 ammo and suitable buckaroo (and adult) guns on hand, so you can rope in entire families.
I don't know if you could get away with shooting IDPA or IPSC matches with CAS gear, but it would certainly be noticed!
Mainly, let the public know where and when you shoot, and that they are welcome to drop in and watch for free.
Have spare eye & ear pro on hand, and someone to greet them and tell them where they shouldn't stand.
Local news media might need some human interest filler to hold for a slow news day, seek them out.
Flyers at local gunshops, especially if they sell Rugers, Ubertis, etc.