Actually, I find this to be an interesting question.
If you have the plastic bags, you have a few choices as to what to do with them. Recycle, reuse or toss.
Clearly, just tossing them is the least environmentally friendly.
But what's the difference between reusing and recycling?
If you recycle, the bag becomes something else. But it takes time and resources and energy to accomplish this, and the process could potentially cause air or water pollution. And there is still a plastic object out there, made out of the plastic bag, that could eventually make its way to a landfill.
If you reuse the bag for pet poop, you are cutting down on the total number of plastic bags bought and used. So the resources and energy for making plastic bags are reduced. But then the bag goes into a landfill and doesn't decompose.
I think a fair bit of research would have to be done to calculate the environment impact of both choices.
What I have done is to reduce the use of what I call "one use" plastic in my life as much as possible. Plastic that can be used and reused, like food storage containers or a trash can or a laundry basket, is okay. Plastic bags, things purchased encased in plastic, throw-away plastic plates and cups, things of that nature, I try to avoid. In fact, I try to avoid "one use" things as much as possible--paper towels, wipes of all kinds, disposable anything.
And then I reuse things as much as possible. And when there is no use left in them, I recycle.
It may not be perfect, but I've been toting groceries home in canvas bags for the last 24 years. I've been using cloth napkins for the same time, and rags instead of paper towels. I'm not a fanatic about it--I use about two rolls of paper towels a year, mostly to clean up cat barf, but I used to go through a roll or two every month.
I don't think there is one perfect answer.
And, while I don't have a dog, just cats, in my town, there is a law about scooping after your dog, so people have to use plastic bags if they walk their dogs in town. On your own property, you can do as you please, but every morning on my way to work, I see many, many dog owners strolling along behind the pooch, the plastic bag of shame dangling from their hands.