Bitless bridles are becoming more and more popular, especially as riders educate themselves more these days and train their horses to be more sensitive (rather than relying on strong bits and gear). The truth is, a horse can be trained to be just as responsive without a bit, as with one.
As for which bitless bridle design to go for when riding flat work and dressage, we recommend the popular 'sidepull' bridle. Please note this bridle is not approved for EA competitions, however it is very effective while still being soft on the horse.
The sidepull bitless bridle still looks and feel very similar to a normal dressage bridle (looks similar to a flash noseband). There are a ranch of brands available that manucfacture them, so you can source them from most horse shops. They also distribute the pressure while still being very effective for stopping and turning which is very important in dressage. Some horses might need a bit of extra sensitive trainging when going from a standard bit bridle to bitless. But you should have a relaxed horse in no time that is more attentive to your seat aid rather than your hands. Don't worry where your horse's head is when you swap over to start, as the horse will naturally go long and low once relaxed and moving forward into the hand.