First question is did you do a prepurchase? If so, and there were no major red flags, I would go down the behavior/training route for now. If not, at least do a basic lameness exam. If for no other reason to see what your baseline in.
To me, this sounds like a baby trying to figure out this whole working life thing. Depending on how long her rearing/bucking lasts, I would push her forward through it and move on with life. Once she learns that there is no benefit to it, it will usually stop. We are finally on the back end of this with my horse with a similar story.
If you’re not confident enough to ride aggressively through the blow-ups (and at one point I had to admit that I wasn’t), it might be better for you not to ride right now. I know that’s a terrible thing to say, but you can still hand walk and groom and lunge her to build a relationship without riding. Either have your trainer ride her daily, or find a brave and capable rider to ride under your trainer’s instruction.
Finally (and this has been life changing for me), learn how to listen to your horse and don’t fight the bad days. My mare usually tells me in the cross ties if she’s having an ants in her pants day. On those days, I free lunge her before I ride. It’s not to get her exhausted, just to let her run and buck and get the sillies out. Similarly, if she surprises me and I get on and feel like I’m sitting on a powder keg, I’ll get off and do the same routine. The important part is to get off BEFORE they do anything naughty. Otherwise you’re enforcing the bad behavior and saying, “If you rear/buck, I will get off, and you will get to have some play time before we go back to work.”
Good luck. This doesn’t sound too out of the ordinary to me, so in a couple months, hopefully you’ll have a completely different horse.