The laptop by itself just barely fits in the bags. If the bags were 1/2 inch narrower it would not fit. The laptop was getting banged up riding unprotected in the bags though, and then walking in I had to juggle my helmet, laptop, charger, and mouse on the way in. The bungee cords hold it very securely. They're tight enough that the passenger seat compresses just a little bit. I would ride it to Florida strapped like that, confident that it would not fall off, but my office is only 2 -3 miles from home anyway.
Maybe there is a special mount for a briefcase, but the bag of bungee cords was only $5 @ Big Lots.