I have one cat. This is what I have been doing for years: I cut a paper bag in half, (I recycle the top part) and place the bottom part next to the litter box and scoop daily. Every 3 days or so I fold the top and dump it directly inside my outdoor trash container. That way I am only trashing 1 paper bag a week. I know this is not the perfect solution, but this is the one that works for me using the least amount of waste and zero plastic. The paper bags I use are made with post consumer recycled content.
I don’t have a dog but this is what some of my friends with dogs are doing: Bring a large piece of folded newspaper every time you walk your dog, scoop your dog’s waste with a large piece of newspaper, make a little “tamale” and then throw it in the garbage. If you prefer plastic, take a look at my plastic bag drawer. I keep all the clean bags from newspapers, bread, pasta, nuts, produce, etc. You can start collecting them too; simply grab one of those bags when you head out to walk your dog. Scoop your dog’s waste and toss it in the garbage.
What about biodegradable bags?
Those are not a good idea if they are headed for the landfill. There’s no oxygen in landfills, so nothing biodegrades there. It is best not to buy something new; just reuse some paper or plastic bags as mentioned above.