What is the explanation behind this answer, might/may you ask?
Is this sentence grammatically correct, if so which should I use and why?
Grammatically they're correct, but the word order is somewhat archaic or poetic sounding: "you might/may ask" would be better colloquially.
With the question spelled out, both options mean more or less the same.
You might ask
anticipates (and preempts) the question being asked, and therefor requires a question being asked nearby (like in your case). It can be used rhetorically.
You may ask
puts more emphasis on the possibility or permission of asking a/that question.