Right...the bit rings...if you mean the rubber discs which fit against either side of the horse's mouth...you take two [pieces of baler tow and loop them through the centre hole of the rubber disc. Then, taking one piece of string in each hand, you pull them away from each other so that they change the shape of the disc's centre hole from circular to oblong...then you work the outer piece of the bit through the resultant space.
On the subject of the horse's feet...it is difficult to give any advice without knowing more about, or seeing the feet, but I would say this...it sounds as if the remedial shoeing was mainly to support the heels and, perhaps, to help take the stress off the tendons. In the long term, the foot will have to be re-balanced and trimmed frequently, so that the heels can accumulate depth, This necessitates gradually shortening the toes and adjusting the hoof/pastern angle as the heels grow down.