Creating a Man Cave in an Unfinished Portion of the Basement

Hello, We have a partially finished basement with one section that is unfinished and we had used it for storage. I decided to take a portion and create a man cave / studio for my guitar etc. Two sections of the wall are concrete while one side is studs with exposed insulation. The ceiling is also just the beams with exposed insulation. My situation is I would like to have a pro drywall the exposed areas but the wife has said no dice. Will the exposed insulation be an issue? I know the fiberglass doesn't get airborne unless disturbed but I just wasn't sure if there was another option until I'm able to put up drywall. I could put up plastic to cover the insulation but then there's the trapping moisture factor.