So I found out one of my head cover bolts is broken. Prolly the nitwits at the auto shop overtightened them when I had a new gasket put in a few weeks ago. I have not been leaking oil. And the broken part is inside the cover, I maybe have about 1inch of bolt that broke off
I read about the extractor bits on here, but I'm worried about shavings falling in, so would I take the entire cover off so i have more room to work with?

 

Drill a hole in the bolt and use a reverse threaded bolt remover to extract.

If the bolt protrudes above the head with the valve cover off, you might also use a Dremel tool to score a line in the top and then use a screwdriver to remove. (or just grab with a pair of pliers)

 

if you're worried about shavings, get a rag and put it all around the area, and get a magnet to keep handy to collect metal shavings from time to time.

 

I assume that you never want to go back to that place again. They should fix it for you of course, but they're likely to make things worse.

Take the cover off and see what you have. Many of these bolts are special double-ended bolts that also hold the rocker arm assembly in place. There is another hex further down on the bolt and you can simply unscrew it and put a new one in.

 

When I bought a 93 Civic, it had a broken valve cover bolt. I used a dremel tool to cut a groove on top of the leftover bolt. I groove it out so I could use a flat tip screwdriver to take the bolt out.