The groomer probably cut/filed the nails as short as they could without cutting the quick (or maybe even accidentally nicked the quick trying to get them short for you), and walking wore them down the last little bit, causing them to bleed. As someone else said, you can use styptic powder or stick from a shaving kit, or cornstarch or flour dabbed onto the end of the nail to cause it to clot more quickly. Also, try to keep the dog calm, as when they get excited, their blood pressure goes up, which makes them bleed more heavily. If you don't have any of those things on hand, even pressure from your finger should stop a nail from bleeding, or they will usually stop on their own after a few minutes if the dog is fairly calm (unless the dog has a medical condition which causes increased bleeding). If can't get it to stop bleeding, or its coming from somewhere other than the tip of the nail, you should head to your vet.
If it is the nail, in the future, you can either ask the groomer to not make the nails so short, or limit walks for a couple days post grooming so as to not wear the newly clipped nails down too far.
