Am I being fair in thinking she should have known?
No, a manager would not necessarily remember what course you have been on, especially if it is a biggish team. Before the review, did you do a self-review and stated that you want more CPD or did you only raise CPD for the first time at the review. If you put it in your self-review, you would expect your manager to have at least read your self-review and come up with some suggestions for training. If she was proactive, she would have checked what you would already have done but frankly, I don't think managers prepare that much in advance for these reviews. If she did not, she could have done better but I would not see it as necessarily a signal she does not value you.
Again, if it is a big team, believe me, your manager usually has barely any time to prepare for these meetings. So don't read too much into it.
I feel really resentful that I've been bypassed because I'm a nice person and try not to make trouble.
What have you been bypassed for? If you asked for a transfer to another team, it is really for your manager to facilitate it (after all, she is hurting her own team for a trained team member to leave). Should you be checking with HR or the new team you applied to? If your manager won't support a transfer and you are stuck, yes, do leave. You said as much.
You say you are nice person. Could it be you are not proactive enough in managing up and managing your own transfer and CPD internally during the course of the year?
My manager is usually too busy to 'manage', so I have to make things happen on my own and update the manager to make them feel in the loop.