Social Security has a Compassionate Allowances list for fast tract approval. I applied for SS disability about a month after I was officially diagnosed and approved two weeks later. Although I can’t specifically find it as bile duct cancer, I’m sure the diagnosis is on the list. My bile duct cancer was/is an inoperable Klatskin tumor.
My disability wait time started from the time I was diagnosed with an “unknown liver disease” (one month before applying) as I did not work past that point. Fortunately for me there was long term disability from work that paid out during the 5/6 waiting months for SSI.
At the time I was hoping to obtain Medicare as our insurance had denied going to Mayo, but as of now Medicare does not start until you’ve been on SSI for two years.
http://www.socialsecurity.gov/compassionateallowances/ 
Here’s another article from the Cure Magazine about applying for disability benefits.
http://www.curetoday.com/index.cfm/fuseaction/journ … ticle_id/1462 