Ok, looking again: It looks like a driving bit (half shank), very commonly used in saddle seat for "work bits", and the dressage rider in me and (and now saddle seat mom), seems to think that to be a double bridle-you need two bits!! Again, looks like draw reins for one set of reins and some sort of martingale, but likely a German martingale for the other set. Looks like a bit of overkill.
When 2 reins are used, but not on two bits, at the saddle seat barn my daughter rides at-the "snaffle rein" is connected directly to the bit and what would act as the "curb rein" is through the running martingale or on a German martingale.
The dressage rider in my is shuddering now that I know all this! Must go drink wine now and try to revive myself.
Just as an FYI that's not by any means a typical saddle seat setup.
More usually you would see *two* reins coming off the snaffle bit, one of which was run thru the rings of a running martingale or (shorter) training fork set down much lower than we would use one in H/J. The purpose of that is twofold: when used by an experienced rider, it's an aid to headset; but it also serves well for beginners to use with a nice soft snaffle bit to get them accustomed to using double reins without ripping the horse's face off with 7 inches of curb leverage.
"The standard you walk by is the standard you accept."--Lt. Gen. David Morrison, Austalian Army Chief
To me, the picture looks like a rein from the hand to the running martingale to the bit, plus an additional draw rein. Perhaps the two reins in the hand is why the rider (or whoever) is calling this a "double bridle" wherever this photo came from.
It is a draw rein run back through a running martingale and a straight (direct rein). It is normal in the saddle seat world to use half cheek snaffles as work snaffles, nothing says a half cheek snaffle is only for driving. It's a schooling set up, and certainly not nearly as complex the the ways show jumpers come up with to put together bits (snaffles, elevators, pelhams, etc.), martingales and nosebands (kineton, figure 8, drop, flash, etc.).
I question the motive of the OP in starting this thread. The picture is clearly of a junior exhibitor. Do you have her parent's permission to be posting this picture? This seems like teeange bullying/ridicule.