I accidentally broke a light bulb, and as I went to go clean it up, I saw my cat licking her lips and then biting onto a piece of glass. I assume she ate a small shard before I got there… is there something I can do? Will it be broken down by the digestive system? Should I get her to a vet?
This is a fairly common occurance. It will likely pass without incident, however to maximize likelyhood of a good outcome you might wanna feed some high fiber food. Canned pumpkin works well; offer 1/4 cup and observe BMs for the next 48 hours. Oh, and BTW IAAV. 
And all this time I thought you were a bridge! 