One thing I learned a LONG time ago in the corporate world (marketing in a MAJOR snack food company where it is cut throat) was to keep a CYA file.
I had a small notebook that I kept with me ALL THE TIME. I documented everything from the most stupid remark or request to the paperwork which was altered to make something look like someone else's idea so they get recognition.
I never really had to use this CYA file but every time I had a review, I carried it with me. It wasn't too long that some figured out that my notebook was a CYA file when they would see me taking notes.
That was way back in the early 90's. Today I STILL have a CYA file. Hubby and I own our company and I still keep a CYA book with things noted as far as requests, pricing info I might have quoted someone, etc. I have used this book for backup, especially when I have had a pricing quote for transportation and then the rep quotes another, higher price when I call to schedule a truck. I also keep a LOT of email documentation and this is used for people like those in transportation to show them a copy of their own email with a quote that they say they didn't make... you get the gist here??
I also substitute teach and I do the same thing every day I am in the classroom.
I would limit my contact with Bill, just be cordial but nothing more. Do your job and if you need to ask a question, make sure you cc someone else who can back you up.
It is up to you if you want to look for another job. Personally, I would dig my heels in if I loved my job and make sure I did the best job I possibly could.
EVERYONE makes mistakes. You should not be "paying" for them forever.