A separate drag bag and shooting mat is a better way to go about this. I have a Voodoo Tactical combo drag bag/mat and it's junk, pretty much falling apart and hasn't seen rough use. I also have a Triad Tactical drag bag that can be used as a mat if necessary (although I never do) and it's been great. It's in my truck pretty much ever day and has held up great. The thing with using a drag bag as a shooting mat is that if you carry other stuff in the bag, you then need to take it all out so the mat can lie flat. Also, the bag gets full of whatever crap (dust, snow, mud) you're out in and then you put your rifle back in it... These days if I'm using a shooting mat it's a thin Tab Gear mat that rolls up small and is unpadded save for where your elbows go. It fits in one of the pockets of my drag bag.
I have one of the browning drag mat cases. It's kinda neat. The whole thing stores in a pelican case for travel. It's got 2 (removable) pouches for ammo and data inside. If your rifle's got a 26+ barrel or you're maxed on butt shims, it may not fit. I've got a 27 inch long action in an A5 with brake and it's nearly a 1/2 inch too short, but I'll get around to modifying it eventually. I think they have it set up for a left handed bolt though. That's the only thing I don't like about it. Otherwise it's not too bad.
The 48 inch NC star bag is...crap. It's 5 inches too short. I've had to resew seams and there are holes forming everywhere. Not recommended.
I've got an Allen Drag Bag and it's just as bad. Resewing needed.
I was contemplating the cadex bag too. Until I see them in person, i'll avoid. I've seen some of the tac tailor bags. They are well made, but make sure you get the right size. The smaller ones are tiny and pretty useless if you have something with a longer barrel.