Can Iphone find my printer?

Is it possible for iPhone XS Max to find and identify a Bluetooth printer as to not rely on AirPrint when given that as the only choice for printing?

Or, is there a way to change the AirPrint only option? It’s not giving me the little box with an arrow to bring up my other options. It’s also saying No AirPrint printers found. I know I can screenshot and print, but I’d like a clean copy.