That is what I put, as well, especially since '今天是 . . .' has been accepted on previous sentences, so input from a native speaker would be helpful, here.
'几月' is not needed in this translation because the speaker already knows what month it is. If the sentence were to be asking for today's date rather than today's number (what day of the month today is), then the inclusion of '几月' would be necessary and correct.
I am thinking of a time traveller (or someone who wakes up from a coma) who wouldn't know what month it is... frankly, I do struggle with this concept.
I think 不好意思 (buhaoyici) is used in a different context, it has an embarrassed, "sorry to inconvenience you" feel/meaning to it. So I guess it would apply here, but like, depending on the context.