There doesn't seem to be a way to manually put on the outfit you get from Jennifer: putting on the harness removes the skirt, and vice versa. And you can't leave the room without wearing both (and the rest of the set) because the game deems the character to be underdressed.
Yeah, the way the clothing items are set up, there's "top" (which takes up the the upper body slot), or "skirt" (which takes up the lower body slot), or "dress" (which takes up both top and bottom slots). I must have fucked up the category when I created that item; apologies, i'll get it sorted in the next update ...
But more importantly, if you're at the point where you're supposed to head over to Jennifer's apartment with your outfit, you're not supposed to actually
wear it right then. She just told you to pack it - and there should be a "Pack your outfit" option open up in your room, which will add everything needed (including the harness, skirt, etc) from your closet to your backpack so you can head over to her place.