Your clients horse actually sounds a LOT like my horse...I have a 7 year old green QH. I bought him last year, I was told he has a buck, but I had ridden tons of bucking horses before no prob and I had an awesome trainer and we both liked him a lot.
Well his buck was when you first tried to get on sometimes before your butt even touched the saddle. After having him two months and coming off a few times and a lot of work we actually got him doing very well! Then all of a sudden he did it again, completely out of the blue, no warning. When he does it his ears aren't pinned, hes not mad, its like hes scared. So we tested him for lymes, its very popular in my area...surprise surprise he came back chronic with decently high numbers. So I got him treated, and he was like a whole new horse. Now he never offered to buck for my trainer, its like he knew...only for me...pain in the ass.
So we kinda believe that when he was broke, he was probably infected...so then associated people getting on and riding with pain...We've come pretty far, had a lymes relapse...retreated...then my trainer moved...so I ended up kinda restarting him myself with the help of a lot of clinton anderson videos haha! Man let me tell you...after that Ir eally did feel like I had a new horse, I didn't have to lunge him before riding, I could just take him up to the mounting block, hop on then hit the trails!
Well last month we had 3 bad incidents thats left my confidence shattered :( I believe now that they half happened because of pain and other half because he was scared becuase I pushed him to do something he wasn't ready for. So after quite a few vet bills hes 100% sound again and very happy...but now I have to find my confidence again :( I've been taking him on hand walks, spending time with him, doing ground work and that all helps. Maybe have your client do some of that too, just spend time with her mare. I was all ready to ride on Monday, got him cleaned up all nice, tacked up in his new aussie saddle, walk the like 1/4 mile up to the ring up the hill....start ground work.....realize I didn't put stirrups on the new saddle...FML lol! so we just played and did ground work and worked on a few obstacles in the ring we hadn't worked on...and it felt good. I'm just taking baby steps now, and my friends coming out to ride him with me this weekend which helps me too.
Back to clients mare....my horse now will kinda test someone though when they first get on...he will stand quietly while they get on, I always make a new person flex his head in for safety...then the second they ask him to move forward he tries to scoot out and buck. Luckily my friends that have gotten on did well and stayed on! When I get on I'm kinda in the habit of instead of asking him to move straight forward, I start on a circle so if he wants to try something I already have his head bent in so I can easily 1 rein stop if he tries something :( I'm still working on perfecting our 1 rein stop though.
Long story short, I know how your client feels, its hard getting confidence back, and babysteps is the best way. I was thinking of sending my horse off for 30 days, and still would love to, but after the vet bills cant afford it for a few more months since I seemed to pick the most expensive trainer :( If you have another horse she can ride that would probably help, if not just do some more ground work and take baby steps. Set up little obstacles she can practice even. Like in our ring we have a bridge to cross, noodles to walk through, a tent to walk through all kinds of fun stuff. Obstacle we're working on now is walking under yellow safety tape while I hold it up for him...still working on it on the ground though. I have to get him to trust me more again so his goto isn't a bucking fit when he's scared and thinks somethings about to eat him haha.