"Ŝi demandas al mi, se mi havas panon" makes sense, doesn't it? "She asks me, if I have bread." I want to make sure I'm not missing something.
"Ĉu" is a standard word which corresponds to English whether/if. "Se" is used like a conditional "if".
I think I finally have a way to remember this! (After several wrong attempts) The second part is the question that the "ŝi/she" asked. And many questions start with "ĉu". Thus the second part of the sentence needs it to represent a "kinda/past" question.