I like to window shop in the tack shop that has a workshop for exactly that reason. My bridle is a sidepull. I used an existing bridle because I liked the reins, softness of the leather etc and just had the nosepiece made up to match. It looks like a regular bridle and I have been on many outrides where no one has even noticed I don't have a bit
Tack is very specific to the rider/horse, so play around with what you have and you will work out what works best for the two of you.
I tried many different versions until I found something my horse was happy to wear. He still prefers nothing but a loose padded noseband (as a sidepull) seems to work best for us. He hates anything that constricts his head movement.