For me, any 180's or ducking and dodging is bad manners and just unacceptable. Especially when alone. I'm not a "horse whisperer" type of trainer, although years and years of dealing with different types of horses allows me to tune into each one pretty quickly.
I view horses something similar to the way that I view children in that there is nothing worse than being around a spoiled, obnoxious or poorly behaved child and it is the same with a horse. You can love those horses, but part of loving them is teaching them good socialization. For me, part of good socialization for a horse is that they understand that certain behaviors are unacceptable. Why? Because you can get hurt or even killed.
The fact that your horse does this when he is alone with you makes me think of two things:
1) If you get hurt by this bahavior when you are alone, you are in serious trouble (and many, many a top horseman has been unhorsed by exactly the type of behavior that you are describing)
2) This is a rider-error issue, which 95% of bad behavior is.
If this were me, the first thing that I would do when I was riding alone would be to get this horse into a bit situation that afforded you much more control. A snaffle just doesn't do it, and the horse knows this.
One thing that you must understand, in order to rid your horse of this dangerous behavior, is that horses aren't people. I know that it is human tendencies to extend a high-level of anthropromorphism to horses. However, doing so can get you killed. I personally know two people who were killed by horses - one of them in a typical situation that you describe (although, being stupid, the rider mounted her horse in the barn - one of the most dangerous things you can do - when the horse wheeled out from under her killing her). Horses are big, strong herd animals that are creatures of habit. They tolerate us because we have trained them to do so. You need to take the upper hand here.
Anyway, proper bitting could take care of a LOT of this problem. The reality is that your horse did it once and got away with it. The bit that you are using is insufficient to control him in this situation, and it needs to stop before you get hurt.
I would recommend trying a gag bit with running draw reins. I would look for a big-ringed, large mouthpiece gag.
here is a nice little article about gag bits, in case you are not familiar with them:http://equisearch.com/horses_riding_training/tack_apparel/english/gagbit_021405/
here is a picture of the type of gag that I would suggest. Though they call it a "polo" gag, I like it because the mouthpiece is big and fat. That means that it is very gentle and a good place to start:http://www.argentinapolo.com/images/picArgentinaPoloGagBit1.jpg
If your horse accepts the gag, which he probably will, and this one isn't enough, you could try a Barry Gag, pictured here:http://www.westernshoppe.com/gen/P13353.Htm
If you are small, and your horse is big, and Barry gag is a great way to go, as it give you a lot of control. You need to have good hands to work with this bit, but it is very effective.
Be sure, if you try the gag, that you fit it properly and use a drop noseband with it. The teeth need to be in good condition with no sharp edges, especially the back top molars. Make sure that you have your horses teeth floated with this bit.
The next thing that you need is a set of draw reins. Here is a good drawing of what they do:http://www.pards.com/store/assets/products/large/03-08-1004.jpg
You should start with draw reins that attach to the girth, feed through the snaffle portion of the gag, and back to your hands.
Why this combination of a gag and draw reins? The combo will help to keep your horses head in place. It is very difficult for a horse to do the dodge move without first dropping and turning his head. Horses that are extremely proficient in the "rollback" (like polo ponies, unfortunately) can roll back on their haunches and spin, but this is an easy move to ride out.
When you ride alone, you should wear this bit/ rein combo every time. Keep your reins relatively short (but not short enough to engage the bit). Keep him on a tight rein, in other words. The first time he tries to tuck and roll, he will find it a lot more difficult to do so.
Now, comes the part that non-professionals don't like. While this bit combo will keep him from ducking and diving without warning, it doesn't address the problem which is this: he's used to doing it, he knows that he can do it with you, and there is no real consequence for it (my guess here).
You must carry a whip. Not a bat. A whip. A nice LONG whip. Like a schooling whip.
The first time that he ducks and rolls on you, his back will be facing the object that spooked him. You need to immediately back him up into this object. He cannot be allowed to escape it. You need to reset his flight impulse.
Back him up into it quickly and roll him back around. This should place him back in the "starting" position, so to speak, where he has to look at this object and decided if he is going to react or not. There will be a moment where he will process this. This is when you need to have both the bit and the drawreins engaged. He will look at it again, and stand for a moment. If he relaxes and remains calm, he gets a "good boy" and a petting. This allows him to realize that he is going to have to look at whatever spooked him - that YOU are going to make him do it, so there's not much point in over-reacting.
However, if he starts to wheel again, you need to smack him - HARD - on the butt with the whip, and give him a good pop with spurs if you were them (which you should). This is going to make him jump forward, so be ready. If he's already tucked and rolled when you whip him, this will be a problem as he'll think that it was his fear object that "bit" him and it will reinforce his reaction. This is the reason that you have to be ready and be holding his head.
Now he knows that there is a consequence for acting on this impulse. This is a good thing. Since we can't put horses in "time out", this is the consequence that we CAN use. And, like children, the consequence has to be appropriate and consistent.
This series has to be done EVERY time he rolls.
back him up. HARD.
Allow him a moment to face the object.
REWARD relaxation and acceptance
PUNISH bad behavior.
Once you get this technique down, he will move towards giving up this behavior. Depending on his smarts and your ability to execute this move, it could be pretty quickly. I would, however, carry the whip and use this bridle/rein combination every single time I ride alone.
Please don't dismiss this behavior. It is very, very dangerous. As much as we want to think that horses are our friends and love us, this really isn't true. They are herd animals who have been conditioned to allow us to ride them. They are trained, good or bad, to allow this. The are large animals and they can seriously hurt or kill someone in an instant. The duck and roll is the equivalent of letting a dog bite you on a regular bases. What started out as an instinctual reaction has become habit and it is a very dangerous one.
Bits, reins, whips and spurs are all tools of the trade. The reason that you rarely see professionals riding without these tools is because we know that they are needed. Horses are much stronger than we are, and these tools help us make our job easier.
If your horse REALLY fights the gag (which he probably won't because your already ride him in a snaffle), you could try something else. I would NOT ride him alone in a hackamore. The action on this can increase his tuck and roll response and it isn't enough control to get him out of the habit.
I hope that you take my advise and take care of this problem. In the horse world, amongst professionals, this is a serious bad trait. Why? Because it is generally unpredictable. Because it can unhorse you. And because if you are unhorsed alone, you can be in danger and so can your horse. As I said, I personally know 2 people killed by this behavior. I have also seen - personally witnessed - horses tearing off after dumping their riders and getting seriously hurt. This is a dangerous habit for you and your horse, BUT it is one that, usually, can be broken fairly quickly.
After he stops doing this randomly, you can start taking him up to "scary things", ready to react, and start teaching him to accept that you decide where he goes and it is his job to behave.