I concur with what Ryan as said. If she was bucking during the first canter of the session, regardless of which rein it's on, I'd be thinking more along the lines of excitement/energy. If she's bucking consistently on one rein and not the other, discomfort or pain would be my first thought.
It may not be as severe as her back is damaged. It could just be a saddle pinching a bit on that rein, or she's not balanced enough to be happy cantering on that rein. It could also be that she has back damage, or like in Ryan's case, the muscles weren't strong enough to properly carry someone properly at canter. Only a vet and/or a saddle fitter could tell you. It might be no harm asking for a farrier's opinion too on whether or not there's something in the feet that's making the right fore, or left rear foot that's making the horse uncomfortable (at some point during canter on the right rein, all the horse's weight are on these individual feet).
Alternatively, it could be a previous injury that has healed, but the habit remains. I would rule out any current problems first though.
Bucking is frequently related to being uncomfortable or in pain. I'd have her back checked out by a vet, saddle fit checked, maybe adjusted by a chiro. If she's good to go in all those respects, work a lot at the trot to the right, doing a lot of bending and suppling work and making her use herself properly and build muscle on that side. I used to have a gelding who did the exact same thing, and the only thing that fixed it was consistent, correct work until he had the musculature to carry himself properly and then riding through it until he realized cantering wasn't the worst thing ever any more. Bucking/rearing/biting/etc is often the only way the horse can say "ow, I don't like that, that hurts/I'm uncomfortable" especially if their subtler protestations have been ignored/gone unnoticed, and we need to keep that in mind when working with them.
Caoimhe Sweeney, sorry for the late response. When I canter her to the left, she has never bucked ( at least for me), but when I canter her to the right, she'll canter for like 5 strides and then start bucking. Also, going to the right is her " bad" direction. She tends to not listen as well when doing anything to the right. When I ask for the canter, I usually put pressure on with my outside leg and kiss, and she'll pick it up.
So when I try to make her stop, my instant reaction is to get her head up since her head is always down low when she bucks ( I don't know if that's the problem- do I need to shorten my reins?) so that results I'm me kind of pulling her, so then she stops cantering. So I think the problem is more of me, since I'm not really sure of how to stop a horse from bucking... Also, is there a way to prevent her from bucking? I'm also the only one actually canter on her, and I only ride once a week ( I don't know if that would be related to her bucking).
Is it always to the right, and never to the left? Do you always start your canter on the right rein?