(a) Are you travelling for leisure or for business? (b) Will you be visiting for leisure or for business? Option A is more succinct, thus that's my preference, but it uses the present continuous tense, which may be less intuitive for native speakers, since we're talking about the future. Option B is also fine, and uses the future continuous tense.

Natives typically ask: "Are you traveling for business or for pleasure?" It's the most common way of phrasing the question here in the US and I believe a few other English-speaking countries.