I'm sorry Molly has been vomiting and know you will be worried for her.
Bobbing that happens just before vomiting can be due to nausea. We'd also consider excess stomach acid and/or stomach pain.
Given the fact she snaffled a rib, I'd suspect this is the cause.
It may be that she is having some trouble digesting it.
There is also a risk of a gut obstruction or perforation.
For now, as long as she remains stable, we should be able to monitor from home.
Offer frequent sips of water and, if you have any, some rehydration solution such as Oralde or Lectade.
If she settles to sleep, I'd monitor for any other signs.
If her signs persist or worsen, a vet visit is important.
If concerned for an obstruction, they can take an x-ray to check if the bone is lodged. If there is a blockage, she could need a surgery to remove it. If not, she may still benefit from e.g. fluids, anti nausea medicine and antacids.