I have a couple of ideas for you. I have some experience with this because it seems like every horse I have ridden is an OTC TB who likes to lean. First thing to do is make sure you have good impulsion (but not too much) - is the horse pulling you, do you have to push the horse with every stride, or are you somewhere in between. If the horse is pulling, the first thing you need to do is get his center of gravity off the forehand and towards the hindquarters, because only when he is correctly balanced front-to-back can he be balanced side-to-side. The best way to do that is with half-halts (I've seen them described many ways, but what works best for me is to commit to a halt from whatever gait you're working at, but change your mind at the last second) and transitions between and within the gaits. Once you feel like your horse isn't pulling on you on a straight line, and you can give with the inside rein, you can start working on the bending. If at any time he starts pulling, go back to the half-halts.
As far as the bending goes, it is important to establish the outside aids first. Sink your weight more into your outside heel (counterintuitive, I know, but it will work) then sweep the horse over with your inside leg. Your outside hand will allow the horses shoulder to move to the outside by moving slightly to the outside before you apply your inside leg. Your inside rein is barely there. Instead of steering the horse from the front, like a bicycle (and what do bikes do when you turn them but lean) you are steering from the back like a sportscar. The horse plants its outside hind foot, reaches under with its inside hind, and lifts the shoulders for the bend. A great way to practice this is to do spirals out - start at a small circle, say 10 meters, and work your way out by "opening the door" with your outside aids and pushing through with your inside leg. I wouldn't do spirals in yet - that could reinforce the tendency to lean. The key is, if you don't want the shoulder to come to the inside, you need to create a place for it to go. Ideally, that place is to the outside, which will give you a more correct bend and make it feel as if the horse is bending around your leg. Keep in mind the horse's anatomy - the spine is a lot less flexible than ours (we couldn't ride otherwise!) and it is the neck and hindquarters that give us the feeling that the horse is "wrapped" around us. You can pull the horse's head around to get that feeling, but the quality of movement will be affected, and if you are bending in preparation for jumping a line of fences, having more weight in the horse's hindquarters will give you better fences.
I'm sorry if this was a long post, but I hope it helps!