How long will it take me to get back to work after arthroscopic shoulder surgery on my writing side?

Depends: It really depends on what you do for work. Since you mention writing, you can typically return to writing immediately after surgery. Holding a pen and writing without raising the arm in the air is allowed with pretty much any shoulder surgery procedure.

2-8 weeks: Return to work after shoulder surgery depends on what needed to be fixed at surgery and a persons job. Most people can return to a desk job with activity limitations in 2-3 weeks. They will be in a sling for 6 weeks. People with heavy lifting, manual labor jobs will not be able to return to full duty for 8-12 weeks or longer.