Well, there are too many issues here to address in one sitting. The GOOD news --- you did not get hurt. The BAD news --- you have done a lot of things wrong. You have done what you would do to turn a horse into a bronc and give them great confidence that they can do it well.
First, you should first teach her to give you her head. People now call it a 'one rein stop'. Then, when a horse bows up and tries to buck, you can snatch their head around and stop them. To pull on both reins at the same time just gives them the leverage they need to launch you over their head. You become the object launched out of a sling shot. You will never be able to out-pull a horse using both reins, but you can make them give you their head to one rein, even if you are not a strong rider.
If you teach this horse to give you her head, you have a chance to stop her from taking up bucking seriously.
Now for all of the 'don'ts'.
1) Don't ever add a new piece of equipment or add a new scary lesson WHEN A HORSE IS FRESH. I have seen many very well trained horses have a come-apart when a back cinch was added when they were fresh. Ride one on a long ride and add a back cinch after you get home. Ride around with it on a tired horse and they learn to accept it right away. If I am going to teach a horse to accept a slicker being put on and off or accept dragging a log or tire with a rope or pony a horse where the rope can get behind them or under their tail, you can bet it will be at the end of a long ride. Their reaction to something new will be 'set' by their first experience with it. You can instill fear or confidence --- the choice is yours and depends how you introduce it.
2) If a horse is 'un-settled', upset (like yours was), has a history of being a little 'cold backed' (like yours does), acts a lot differently than it usually does, WARM THE HORSE UP. EITHER TROT AND THEN LOPE SEVERAL CIRCLES in a confining area, (where it is easier to pull a horse around and stop it) before heading out in the open where you are more at the mercy of what the horse decides to do. I will lope very 'fresh' horses or horses that I have not ridden in several weeks
3) If you are not a well balanced 'good' rider, you should warm an 'un-settled' horse on a longe line or in a round pen WITHOUT A SADDLE. Trainers call it 'knocking the air out of one'. It makes a really 'fresh' horse much more settled and not have as much 'feel good energy'. NEVER let a horse buck with a saddle. Some get it out of their system (as it is sometimes called) and other just get practice and learn to like it and do it more and better. So, I think it is very important to NOT let any horse practice bucking.
4) If your horse is stalled and has not been ridden in a while, TURN IT OUT to run and play BEFORE you saddle it up to ride. Remember that any time you are handling or attempting to control a horse, it should not play or behave in a uncontrolled way. That means that the longe line is not for running and playing -- it is for serious work. If you cannot control a horse on the end of a rope, you probably cannot control it very well under your saddle. It means you need to learn how to control a horse in all situations or your relationship is a ticking time-bomb.
I have to go now, but I need to show people how to put a type of 'over-check' on a horse that they can be ridden with. This stops a horse from lowering its head which it has to do to buck hard. I just have to get to an appointment now.