The bosal actually does not produce any leverage. There is nothing for it to leverage against. It tilts and shifts on the nose, but it can’t produce leverage like a shanked hackamore that applies leveraged pressure around the jaw. It is a signaling device and can produce fantastic results in the right hands.
The rope halter functions a little like a bosal, but it doesn’t hold its shape nearly so well or provide much spring to return to shape. The bosal, rope halter, and shanked hackamores are not designed to maintain contact, but in the case of the bosal you don’t really have to pick up full on straight-reined contact in order to communicate.
There are bitless designs that are more conducive to contact. The ones I most often see for Dressage outside of a sidepull are the wheel hacks, also called “bitless bits” such as the LG Zaum, Orbitless, Flower, and Star Wheel. They have multiple slots that allow for settings from sidepull (direct nasal pressure) to mild and moderate leverage. I haven’t used these much yet, but have started our yearling on the long lines a little with a Star Wheel.
I personally like continuous rein cross-unders. Somewhat like the Dr. Cooks, but instead of the ring to connect your reins to the reins form a continuous line with no interruption. You can pick up and work a contact, get reasonable feedback from the horse. I find my crew are more forgiving of mistakes bitless, more freely forward, and if there is a differing of opinion it is less frantic or explosive tban with a bit.
There are also scawbrigs, like the LightRider that use pressure from a “floating” strap on the chin groove initially before engaging nasal pressure.
There is one design that is touted essentially as a double bridle that has a sidepull and the scawbrig built into it working as the snaffle and curb respectively.
There are a whole lot more options to riding bitless than there used to be!
I like riding bitless and feel like I get a good response from my horses and no real need for the bit other than the fact that USDF insists that it is needed to qualify in competition.
I’d love to see USDF and the FEI both to realize that the horse really should be “on the aids” over “on the bit.” Working Equitation allows for bitless riding in all phases, even the Dressage. Other countries’ national organizations appear to be moving towards allowing bitless riding too, the Dutch being the most prominent.
In short: Yes! You can do Dressage (well!) bitless!