Hello, my name is***** and I have over 20 years of experience as a veterinarian. I am sorry to hear that your girl GiGi ate some cooked rib bones.
The trouble with cooked bones is that they are more brittle, thus more likely to splinter and cause a perforation. That is true of some bones more than others and unfortunately rib bones are more likely to splinter compared to some others.
The other concern is an impaction of bone pieces or blockage due to bone chunks getting stuck.
While I understand that getting those bones out would be nice I do not recommend inducing vomiting in cases where dogs eat sharp objects like bones. The chances of tearing her esophagus or stomach or causing a perforation as they contract to force the bones out with vomiting is much too high. I hope she at least chewed a little before she swallowed as that will make passage a little easier.
In this case we need to try and hope that we can get these bones to pass through her gastrointestinal tract, and that her stomach acid helps us by dissolving the fragments.
To help I recommend starting with a vaseline sandwich. Take half of a slice of whole wheat bread, slather with vaseline as you would peanut butter on a slice of bread, cover with the second half of the slice. Feed it to her bite sized piece by piece or she will make a huge vaseline mess. This adds fiber and hopefully makes the bones pieces slip rather than catch.
For the next few days, until the bones pass, she'll need to be fed a bland diet with lots of fiber added in small meals several times a day, 4 to 6 meals is ideal. We do this so the bone pieces are surrounded, the gut isn't irritated scraping just against bone splinters, and the bones are part of a chunk of ingesta.
A homemade diet for this is 1/3 boiled, lean hamburger or boiled, white, skinless chicken, all fats and juices drained off the meat, and 2/3 boiled white rice. Add 1-2 tablespoons of canned pumpkin, (not pie filling, just pumpkin), to each meal to increase fiber/bulk.
You'll need to check her stools frequently for bone pieces over the next several days. I would expect her stools to be a little loose but they should not be black or tarry, as that indicates internal/intestinal bleeding.
Signs that things aren't going well, and she needs an immediate veterinary visit, are vomiting, a tense painful belly, lack of an appetite, a fever (more than 103.5F rectally), large amounts of blood in the stool (a small amount if she feels well is something to just monitor) or black tarry stools, and lethargy.
If you aren't seeing bone fragments in the next day or two a veterinary visit and an abdominal radiograph to see where the bones are is an option. If it doubt at all that things aren't going well it is always best to have her checked.
Once the pieces are passed and she's feeling well then start mixing in her regular diet, adding a little more regular and less bland at each meal. It should take a week or so to get her converted back to regular food.
Please let me know if you have any further questions.