That's a nice-looking mare.
It sounds to me like you need to continue her (and your) training at a walk and trot before you start cantering. Horses are like people. If you've ever watched someone start learning how to jog for the first time, you can plainly see they lack coordination of a real runner. It takes time for their body to gain the coordination and smooth things out. Horses are the same. Too many people, particularly novices, just want to get on a horse and feel the exhilaration of galloping around the arena or across a green field, etc. Some people will say that horses run all around when they are foals and know how to do it. That is true, except that they weren't doing it with an extra 150 lbs or so on their backs then. The have to develop the coordination to get all their muscles working together to handle the weight of saddle and rider. It takes time. Some horses longer than others. Some horses are just more coordinated than others.
While we're on that topic, you also need to learn to move with the horse. If you learn to keep your seat at a trot, you will be able to handle the canter better and your movements won't be fighting against the horse.
Be patient with her and with yourself. Spend a couple weeks at a walk, just getting her used to your cues. Teach her and make her obey your cues at the walk. Then move to the trot. Make her trot at the speed you choose. Teach her to hit that nice easy jog that is so comfortable. It will take a while to get there. Once you have got her coordination and her obedience up to speed at the trot, then go to the canter. It will take her a while to smooth out at the canter. Hit the canter and make her slow to the speed you want without dropping into a trot. It will likely be quite rough at first. It will eventually smooth out as she learns.
Be consistent with your cues and commands. You have to be firm with this. A horse will only learn to do things as precisely as you make them perform. You must be firm and consistent. You have to know what you want the horse to do and you must have a definite and consistent cue to tell her what you want.
Now, another thing that will affect her smoothness at the trot and canter is collection. That's a whole other topic. A horse that will give to the bit and bend at the poll for you will be smoother than a horse that will not. Bending at the poll and lowering the head to about the withers level causes them to pull their rump under them a bit and move in a "collected" manner, as opposed to "all strung out." That takes some good training and many horses, particularly those used only for trail riding, will never learn it.
Now about the crow-hopping. If she hasn't bucked you off by now, she's not serious about it. Just ride her through it. She'll eventually give up on it, because it wastes energy. Horses don't like to waste energy if the effort gets them nowhere. I'm sorry to be argumentative, in my experience and opinion, getting off when she crow-hops is the worst thing you could do. Just ride her through it. You'll gain confidence and riding skill and she'll realize it doesn't get you off or benefit her in any way. She'll eventually get over it.
Remember, horses are a lot like a two year-old child. They will learn every button you have and push them as often as they can. If you don't react to the buttons, or if they have an uncomfortable experience when they push them, they stop doing it. Firmness and Consistency are the keys.
By the way, the mare in my avatar is a 7 year-old I bought last year as a green-broke and have been working her through the same thing. I started working with her regularly in July. I worked her at a walk for two months or more before starting the trot. I graduated to the canter last week. She's smoothing out already.