I believe I've seen this sentence in two forms in this lesson: "Ŝi demandas min..." and "Ŝi demandas al mi..." I was starting to think that the preposition 'al' was required with the verb 'demandi' but now I see it in this sentence without. Can either be used? Do they have the same meaning?
They both can be used, but as a literal translation, "Ŝi demandas al mi..." would be like "She asks whether or not I have bread to me". But saying that is very unnatural. The only thing to be mindful of is they when using "al (pronoun)" that the pronoun remains nominative (or technically dative).
Prepositions don't always have direct equivalents from language to language, and remember that English is the highly irregular of these two languages.
The preposition "al" doesn't just mean "to," it means "in the direction of." In this case, she's asking a question (d.o.) and she's doing so "in the direction of" me (i.o.). If you wanted a one-word equivalent for this sentence, consider "She asks of me," although you wouldn't use "de" because we're not indicating possession or origin.
It's often important to divorce your native language from the one you're learning and think of the latter in the abstract; just because a sentence doesn't have an easy "word-by-word" equivalent in your native language doesn't mean that it's wrong on its own language.