Not exactly a Rosh Hashanah or Yom Kippur story, but for some reason it springs to mind.
My grandmother (mother's mother) was traveling back from our house on Long Island to her place in the Bronx on the Long Island Railroad. (She would then take the subway after she got off in Manhattan.) It was 1966.
She didn't realize for the first few moments that about ten rows in front of her were sitting our (my brother's and my) shule teachers. (Shul-eh, as opposed to shul. The Shule -Folkshul or folkschool movement- was started in the 1910's by Jewish Socialists or socialists who wanted their Americanized or American children to receive knowledge of Jewish history, culture and, yes, religion too, as well as Yiddish and/or Hebrew, and also a knowledge of the progressive movements of the time. It would not emphasize prayers, but would also provide knowledge of the different groupings in Judaism.)
My brother and I were attending a Workmen's Circle shule in East Meadow, on Long Island. I appreciated it a lot. My brother was not exactly enthralled.
She heard my teacher say: "Ikh hob di shvester. Feyge. Vos far an ayzerne kop!" (I have the sister, Feyge (my Yiddish name). What a brilliant mind. Idiomatically, what an iron head (holds onto knowledge and does not let go).
Then she heard my brother's teacher say: "Ober ikh hob di bruder. Oy, iz dos a bandit!" (I have the brother. Oy, is he a rascal. Since my brother's favorite pastimes in shule were throwing paper airplanes, jumping over desks and opening and shutting the window, "bandit" may have been kind.)
My grandmother knew them, and they knew her (from various places, summer camp among them). She pushed her hand hastily against her mouth because she didn't want them to hear her laughing and she didn't want to embarrass them by somehow showing that she had heard them. (She thought their summations quite accurate.)
Somehow she managed to keep her head lowered so that they did not see her during the entire ride. She told my mom over the phone when she got home amid the laughter that she could now let out.