You need to present the user acceptance step as something that benefits the customer, not you.
You have been talking about the benefits to your company ("we require user testing to confirm the change/bug is working as the user expects", "we are not allowed to release live without user validation"). It's not surprising that the customer feels like they are doing work for you. This, after (in their mind) you failed to address their needs in the first place, by releasing something that wasn't what they wanted!
You can start by explaining that this is a key part of the process that benefits them. Imagine how much worse it would be if you released a "fix" and it still wasn't fixed, or working in the way they wanted! Imagine if you'd accidentally made it worse!
There was clearly a breakdown in communication that caused the bugs in the first place. If you had perfectly understood what they wanted, you would have perfectly tested against those expectations yourself, and released something that was... perfect. They found a bug. That means that whatever process you have for them to request a feature and you to provide it, missed something. It isn't sensible to assume that the process to report the bug and get it fixed, can't possibly miss something too. The sensible thing to do is to double check: "we think we've now done it as you wanted, is this right?".
This is especially true if they are paying for any of these changes or fixes. This is an opportunity for them to ensure they are getting their money's worth. If you release something, and it's still not what they want, you'll have to go through the whole process all over again, and charge them again. Wouldn't it just be better for them to confirm the fix before releasing, so they only pay once?
In any case, it needs to be explained to them as a positive opportunity for them to have their input, not a drain and demand on their time for no benefit.
FWIW, I think it's a bad idea to argue by analogy, as other answers do, because you end up talking about something that isn't actually the problem you should be talking about. Even so, if I took my car in to fix a flat tyre, I'd have a look at the tyre before driving off, to make sure it really did seem to have been fixed. Otherwise, if I just started driving and noticed it was flat a way down the road, the garage might say they did their job right and the new tyre must have gone flat after I left.