From my own experience, the initial investigation may be just a short sigmoidoscopy that takes about ten minutes.
In most cases of, say, ulcerative colitis, inflammation starts in the rectum then spreads up through the sigmoid colon into the descending colon then into the transverse colon and so on, as the disease progresses.
A rectum and sigmoid colon showing no signs of inflammation or any other disease would signify that the examination need go no further. If there is evidence of disease then the longer examination taking about 40 minutes would be required.
Discomfort around the “bends” is quite normal. The tube is having to negotiate sharp corners. A nurse will often manipulate the patient’s abdomen or position on the table to easy the passage of the colonoscope.
It's why I would always advocate trying to have the procedure done without sedation if possible so that the patient is fully aware of what is going on, can watch the progress on the screen and ask questions. Entonox is always to hand to easy any temporary discomfort.