The very short answer is, "No. Don't waste your money." Use whatever you have on hand (pardon the pun) to clean up after your dog when you take her out for a walk.
I've mentioned before some of the worst things that a recycling specialist can hear. (I should do a separate post on that!) but one that crops up fairly regularly for me is, "I buy those special biodegradable doggy poo bags!" I added the exclamation point because people are usually so proud of themselves for this purchase. The truth of the matter is that the doggy poo is likely going to the landfill, correct? If it goes to the landfill, not a lot is going to happen. Landfills are created specifically for safety first and that means not a lot gets in or out of them. In other words, the conditions you need for decomposition (light, moisture, oxygen) are simply not present in landfills. So, what is Fido's poo doing in the landfill in that special bag? Much the same thing it would be doing in a plastic sack. Or a paper one. Or a plastic glove. Or grandma's china. It's just sitting there.
So, don't waste your money on biodegradable doggy poo bags. Or anything that has a claim of biodegradability that will ultimately end up in a landfill, for that matter.