A bitless bridle usually has a part to the bridle that crosses under the horse's cheeks and attaches to the reins. That way when you pull on the left rein, pressure is also applied to the right side of the horses head to "push" his head to the left. It also applies pressure to the top of the head when you pull back on both reins, which I have seen referred to as a "hug" effect and is suppose to help with stopping.
A side pull is exactly like a halter with clip on reins. I personally like the side pulls better. A plain leather one, that is just like a halter, is only better in that a halter may not fit high enough up on the horses nose and the metal pieces may hit him in a sensitive area of the face and the side pull fits a little snugger then a halter and does not slide around as much. I have never used the ones with the single or double rope nose bands or the rope halters with knots.
I ride in a halter w/clip reins at time in our arena or in the pastures, but for trail riding I don't think I would trust it. A side pull gives you a little more "umph" and it doesn't move around on the horse's head like a halter can. I use a cross-under style bitless for trail riding, similar to the Cook bridle.
It works OK, but you obviously have less force available than with a bit. I tried one with the cross-under-the-jaw thing, but didn't like it because it didn't release consistently.
One like this runs around $20-25 on ebay. If it didn't work for you, it remains a perfectly good halter.
I would not use this particular set up. Look at where the contact is? The the nose and side pieces are creeping up to the eye. The contact underneath has moved up the jowl. In order for this to be effective, the main unit (halter, headstall) must stay in place for consistent signals to the horse.