What you should've said, I reply, is "I decline to answer that question on the grounds that it may incriminate me".
But, she replies, I want to be polite. But that is polite, especially if prefixed "I'm sorry, sir, but I decline to answer the question ...". Indeed, you should always be very polite to cops. Standing up for your rights is not being impolite. They might not like it, of course, but this is far different than flipping them off or calling them facist pigs.
The waitress doesn't accept my argument. Instead, she says "What I should've done is said that I hadn't been drinking". NO NO NO! Don't EVER lie to cops. This invariably gets you into worse trouble. It's like five year olds who think they can get away with lying to their parents -- you can't. But luckily, in our system, you don't have to. All you have to do is stand up for your fifth amendment rights.
"But doesn't that mean I'm guilty?", the waitress asks. No! That's a paradox: if refusing to incriminate yourself incriminated you, then it wouldn't work, would it? The cops are quite used to this. They know that innocent people refuse to answer questions all the time. Indeed, in cop school they are taught to ask incriminating questions, knowing that you are too stupid not to answer. They always ask "Have you been drinking?" because they know stupid people will answer. While they might be unhappy that you don't answer, they won't consider it insulting or proof of guilt.
Even if you haven't been drinking, you should still not answer the question! I drink almost never (I order diet coke in bars), so the correct answer for me is "no, I haven't been drinking". But I still refuse to answer the question when asked by cops. It can only get me intro trouble. If I give the honest answer, and the cop later claims in court I was slurring my words and stumbling (indicating I was drunk), I can still get into trouble for lying. Indeed, I know somebody that happened to. He would've been convicted, too, had it not been for the dash cam proving he was stone cold sober, and that the cop was lying. By the way, that video had "accidentally" been deleted, but a backup copy was later found.
When a copy pulls you over, #1 put your hands where they can see them (so they don't feel afraid you are going for a gun), #2 be polite, #3 follow their directions (that don't infringe on your rights), and #4 NEVER EVER ANSWER THEIR QUESTIONS.
The waitress remained unconvinced at this.
Update: Bah, Scott Greenfield has this to say about this post. In general, he doesn't like us non-lawyers advising people about the law.
@ErrataRob It was partially inaccurate, and moderately wrong. So it could have been worse, but it could have been much better.
— Scott Greenfield (@ScottGreenfield) November 23, 2013