Have a look at the German Training Scale. It's a Dressage thing yes, but it applies to most disciplines.
Rhythm and Relaxation are the first two steps on the scale. The horse should travel freely forward, maintaining it's rhythm and tempo.
Then you step up to Connection, Impulsion, Straightness and finally Collection.
To get correct bend, you cannot just pull on the right rein and expect the horse's body to bend right, and vice versa. Pull the right rein and chances are your horse's head will look to the right, but the wither (and rest of the body) will continue to the left.
The hind legs are the horse's engine. Trying to steer and bend without having the engine running is like expecting to get around a turn in a car without the accelerator on. Maybe if you're on a bit of a downhill slope you'll get a bit of speed and be able to drag the car around the bend, but it's not going to be as easy as if you've got your foot down, to push the car around the bend.
If you can establish forward, while riding your body along the line of the circle, you will be surprised at how easily the bend will come. Teaching some steps of leg yield on the circle will help to develop an inside leg-outside rein connection, which will then assist in developing the bend through the ribs. You can then move onto shoulder fore, which will develop even more flexibility through the body.
Bend is balance. That is why smaller circles are not introduced in a Dressage test until a couple of levels up, and ever later in canter. The tighter the turn, the more bend required and therefore the more balance and collection in order to maintain that bend without losing balance. Either through throwing a shoulder to the outside, dropping an inside shoulder, swinging haunches out etc.