I love my sidepull bridle from Running Bear. I generally ride without a bit on the trail, but I use a bit when I’m doing dressage/arena work. It’s constructed like a halter with a padded noseband with rings to clip the bit onto. It’s also got bit hangers if you want to go that route. I often start out doing whatever arena work with a bit, have him bend his head around and unclip the bit from the saddle and then go wander around to cool off and let him graze bitless. You can easily put a rope halter under it, but it isn’t necessary.
Mine is several years old now and I just toss it in a bucket after a ride then wipe it down or throw it in the dishwasher and it looks brand new.
Someone said biothane doesn’t break, but mine has all brass hardware. So, while the bio won’t break, there are plenty of fail points. My horses have broken several leather halters over the years and the points that usually break are the brass hardware so I’m not overly worried about the unbreakability part of biothane.