Sounds like you really want a cheapo Tyvek/Polypropylene or similar bag like what are handed out at trade shows. Check out discountmugs.com and you can get samples without logos for like $5.

I used to carry one of these packed in my TravelPro Crew 9 20" so I could keep the laptop in the front compartment and still have something to carry when going in to clients. Unfortunately the weight in the front of the Travelpro made it prone to tipping and I ended up ditching the laptop all together for a Surface Pro (that now resides on top in an Amazon Basics 11.6" bag).