Anticipation and pulling on the reins is a common problem a lot of lesson horses have because they are used to being able to get away with things and do what they want because they are only being ridden by inexperienced riders. Even seasoned lesson ponies should be ridden periodically by an experienced trainer to keep them respectful and responsive to the rider. At the barn I used to work at that was one of my biggest jobs, I rode the lesson ponies on a regular basis and made them work hard to gain their respect so that they would respond better to the children that rode them. There was a huge difference in the horse's behavior when I had ridden them the day before as opposed to when I had not ridden it in a couple weeks. Does your instructor ride the horses you ride on a regular basis?
This is the second post of yours that you have talked about trouble you are having with the lesson horses you ride. Both cases sound like problems with the horse's training, not your own riding. How long have you been taking lessons with these horses? Is this the first riding barn that you have ridden at? If you are having problems with the horses you really need to talk to your instructor because she will be able to help you the most directly. These training issues are not something a beginner rider should try to deal with on their own. (I am assuming you are a relative beginner).
If after talking to your instructor she is not able to help you I highly suggest you try to find a different riding barn to take lessons at. You need to learn to ride on a horse that is respective and responsive to your aids. Riding horses like what you described will only result in you loosing your confidence and possibly getting hurt. Not everyone out there that calls themselves a riding instructor or trainer is actually qualified to teach or train. ANYONE can call themselves a trainer, even if they have only ridden a horse a few times. Just because they own horses does not mean they know what they are doing.
Now, I don't know your trainer, I've never seen the horses you have ridden. I do not know the whole situation. I'm not telling you right now to leave that barn. I can't know for sure unless I have seen the place myself. But it something you should think about. Get the advice of some more advanced riders you know. Look around at different riding barns in your area. If you do decided to switch barns look for a place where the instructor actually rides her horses (I once took lessons from a lady that had not ridden a horse in years. The first time she got back on one she fell off and broke her collarbone. I left that place pretty quickly). Ask if you can watch someone else take a lesson before you commit to taking one yourself. If they say no, be suspicious of them and look somewhere else. Look for horses that are quiet and responsive when being ridden. There should be very little head shaking or pulling on the reins and the horse should go where the rider tells it to at the speed the rider tells it to. The instructor should seem in control of the situation at all times and not seem flustered. She should be able to give easy to understand instructions, should not yell all the time, and the riders should look like they are having fun. That is the kind of riding classes you want to ride in.
I know it might be hard for you to leave the barn you are at. You must be attached to Buster. I know I got very attached to the first horse I rode, her name was Shelby. I cried when I left her, but it was for the best. I'm telling you know, there are plenty of wonderful horses out there for you to fall in love with. What is important is that you establish a good foundation on a safe horse that will build up or confidence, not tear it down. The first few months of your riding experience are the most important months of your life. That is when you will establish ridding habits that will stay with you for the rest of your life, both good habits and bad. And let me tell you, it is hard to break the bad ones once they are ingrained.
Sorry for the long post, I hope I was of some help.
I refuse to let adventure leave me in the dust. The time of my life is out there, I just have to go get it.
See My Blog: Dream Chaser