There are none. HA! No one specifically makes dog disc bags. But, there are excellent alternatives, as you are about to discover.
With hitting up disc dog club events, competitions, and practice, I think you may find out that you need a few things to take with you when you head out with your pup to play disc games with.
First and foremost, is water and water bowls. We lug a 1 gallon jug in a backpack everywhere we go. The back of the truck has five more. (Usually for events, not practice.)
You need shade, but that's for another post. You might need chairs. (They make shade and it's a spot to either sit down at or hang your jump vest.)
And there's your dog discs. You need something to carry your dog discs in if you get enough or, in carrying everything else, you find you cant' wrangle loose discs.
Welcome to the club of disc dogging!
Like I said before, there are no disc dog disc bags. But there are great alternatives that you can find that are designed for Disc Golf. The only thing you need to do when you get them home, is not insert (or pull out) the pre-fabricated disc holders, and walla, you have a dog disc bag!
I've experimented (it's the best word I can come up with) with a few kinds of disc bags.
The first up, because it was pretty inexpensive and an easy start-up bag, I picked up the Innova Starter Disc Golf Bag. (Yes, our dog discs fit perfectly.)
They're $16 on Amazon and can be pretty handy. (Innova-
With the exception of the zipper, it's an awesome starter bag. But the zippers suck. I can unequivocally say that. I bought two over the span of some time and both of them, their zipper sticks and doesn't "zip" very smoothly. Just this last weekend I ran into other people with the same bag, and they all had the same thing to say about the zipper.
But for all intent purposes, it's an awesome starter.
I have two of them, and for quick runs to the park or what not, it's perfect.
But all in all, it's a good bag and it ran me $45. (Fade-
So the Fade bag works, but as you can see in the image, it's a little bunchy. But hey, bunchy is better than doing a balancing act with 20 discs in a shopping bag looking like a confused homeless guy, right?
But then I started practicing at work and even though this Fade bag is my main bag, I ended up getting yet one more (my last) bag so that I have something for my practice discs that I keep at work and play with at the park nearby.
At first I was hesitant because it was another Innova bag, and remembering my horrible experience with the starter bag zipper, I held back for a bit. But I chatted some folks up and they didn't seem to have any complaints.
The zipper is perfection on this bag and it better be, for the $65 price tag on it. (At the time, I had a huge discount. Had I not had the discount, I would not have taken the chance on this bag just because of my zipper experience from my previous Innova bag.)
But it's awesome. It's a bit heftier, easier to carry, more square and does not bunch up and is a solid performer. I use it almost every day and love it. On Amazon: Innova-
If you have the bucks, the Innova Champion bag is the way to go. If not, the Fade bag works just as well, but just feels slightly less solid. But it's not.
Budget minded folk might want to think about that starter bag and just never zip it. It has a velcro strap system that allows you strap it open permanently.
And in all seriousness, one of those commuter bags you get from "ride to work" day or a decent backpack will do just fine too. The only thing I'd warn against on those options to make sure your discs either lie flat (stack) nicely, or they're standing up nice. Because if you store them in such a way that allows contortion to take hold, well, you will not enjoy the aesthetic appearance of a wobbly disc in the air. And your shot will go to *whoop!* in a handbag.
(The prices I mention are Amazon Prime prices, so I am not sure if the distributors of the above bags are being like some of those that jack up the price to absorb "shipping" costs or not. Yes... they do. I saw reports, then experienced it myself. Here's what I had to say over on Consumer Bits: Supposed Free Shipping from Amazon Prime Vendors.)