Put wheels on it.
If you're going to put them both in one box, either put wheels on it or get a cart. I put my Protektor Doctor with Handle in it's own Stanley tool box where I also put ear muffs, ammo and various light odds and ends. The bag alone weighs 22 pounds. For my rest I built a custom box that holds both my Shade Tree joystick top and a windage top. That's another 20 pounds. To take things to the line, I use a Foldit cart from Kotulas.com. I highly recommend it for bench rest, service rifle and F-class. I also use a doctor's exam stool on which I built a platform on top of the legs. When my relay is done, I put the rest on the seat and ammo, timer, bag and everything else on the platform. I then just roll it out of the way.