I by no means am an expert, but I believe that if you are using a woven you should cut the fabric on grain.
Lightweight jersey is often cut on the bias particularly when making a Diane Von Furstenberg type wrap dress. I makes the fabric drape into nice folds. But in my experience, when I have mistakenly cut woven fabric a bit off grain, it would not drape correctly and would twist and pull.
Don't start cutting quite yet. Wait for some of the more experienced garment sewers to weigh in on this question. You are sure to get the right advice.