The Exciting Game With One Rule

Nope, and you are in violation of the rule.

You are not in violation of the rule.
I’ve played it as Grandmother’s going on a Picnic, with questions about what’s in her basket.

This is more of a “word with double letters in a prepositional phrase” rather than “don’t say bad things about white bears”.

Just so we’re clear: it’s don’t say anything about white bears. Don’t even mention them.

On with the show…

Be that as it may, your post was not in violation of the current rule.
And neither is this one.

Is there some good way beyond just random guessing or the 20 questions approach to get at this new rule?

Well, it has to do with the wordplay property of a particular type of word, rather than grammar or punctuation.

Your post did not violate this rule, nor does mine.

Does one break the rule when they try to guess what the rule is?

IE: The rule is not to guess the rule.

No, but you didn’t break the rule. It doesn’t have anything to do with the sense of the sentences either.

I have not broken the rule here.

No words over three syllables.

That’s getting closer, but not it. You are in violation of the rule, though.

No sentences under ten syllables?

That’s not it, but it doesn’t violate the rule. It’s about the nature of one or more words in the sentence rather than the sentence itself. This post does not violate the rule either.

May we determine the rule by May?

That does not violate the rule. It’s about the characteristic of certain individual words.

Will bells ring for thee if we use double letters?

Since double letters were used in the last round, I didn’t use them here.
Your post violates the rule, though.

Is the rule about words which may be used as nouns or verbs? Ring up the ring.

No, it isn’t, but good try. Your post does not violate the rule, nor does this one.

Is it fair to ask if the rule violation occurs in the first part of the sentence,

“Will bells ring for thee”

or the second? “if we use double letters”