I don't see it quite that way. I don't see anything at all wrong (in fact I think it's a positive thing to do) to approach somebody and say something like:
"I didn't say anything at the time, but you know what? It really hurt my feelings when you said X last year on my birthday."
It's best to clear the air, I think. Even if that person says, in response, something like:
"Yeah? Well, let me say it again. I still think X."
My policy is to get the cards on the table and see where people really stand. Best if done at the time, but, better late than never if it's bothering you.
However, that's not PQ said.
Of course it would be appropriate to go up to someone at let them know that something had been bothering you.
PQ said she wanted to ask that person to go out for drinks (or some other equiv. that would involve the other person changing their schedule, make plans) to talk about it.
If you want to tell the person, make it at their convenience, not some event were there is a meeting so they are a captive audience to your drama.
It's potentially putting the person out.
This may be a silly example, but I've had the following happen to me twice. The first time I was taken unawares, the 2nd time I remembered the first time, and said something.
I both cases, I loaned someone (2 different people, this was years apart) a small amount of money, because they where temporarily short. They got handed cash.
In both cases, the other person, a few days later, wanted to write me a check. The first time I said "oh, um, all right" Then I was the one to have to schlep to the bank, when it was open, so during my lunch hour, to cash or deposit some small check, or after hours at an ATM.
The 2nd time when the person came up to me and tried to hand me a check I said "I loaned you cash, and I'd like it back in cash. I did you a favor loaning you cash when you were short, and now you're trying to make me go out of my way to get my money back. If you don't have the cash, I'll wait. I'm not worried."
The funny thing was, the other person said "But I'll have to go to the bank to get money." Well, yes you will.
In other words, if you want to do something that is meant to make yourself feel better, in this case unburdening yourself of a grudge, don't make the other person part of your play.
When the time is right approach them, and get it over with. Don't make them drive across town, or even cross the street to listen to your problems. And it is your problem if you've got a grudge, not theirs. The action may have been theirs, but the grudge is all yours.