Since we use reusable bags now, we don't have many disposable plastic bags to use in cleaning up after our dogs. This isn't really a problem in the yard, but what is the easiest way to pick up after your pet when you're out on a walk without using plastic bags? I hate buying lots and lots of those plastic poop baggies (I really don't buy it that they are biodegradable).
I would consider using a small bucket with a cover.
They can easily be carried and the cover will restrain the smell. Also they are easy to clean with some water outside.
For practical considerations: You could take a small shovel in it, or just use the cover to get the poo in the bucket, although I think the latter will require some exercise before it can be done properly without spilling some on the outside of the bucket or cover.
On walks, we just use the disposable plastic bags in a roll that are made for dog waste.
They aren't biodegradable, but since we dispose of the waste in the municipal trash, I don't think it makes any difference - modern landfills aren't designed to promote biodegradability. The local municipality specifically forbids dog waste in the municipal compost bins, they want it disposed as trash.
Since the dog waste bags are smaller than plastic grocery bags, if you were previously using the 'free' grocery bags, there's still a net environmental win by using the smaller dog waste bags.
When I used to live in the city and had a much smaller dog who would generally poop close to home, I would take a Kleenex doubled over and use it to pick up the waste, then I'd flush it when I came home. I'm not sure if that an environmental win for the environment due to the water usage.