I am sorry that my original answer wasn't thorough and reading it again myself it isn't precise; as always there is a lot more to say. However, I wouldn't have thought that there is a restriction in the flexibility of your common bile duct (CBD).

The figures obtained during ultrasound investigations vary greatly from person to person. I provided some figures to indicate how flexible the CBD is and how it can expand. About 50% of people will have a CBD that measures 6.1mm of less on an ultrasound. The common bile duct may have any reading between 3mm or even less and 15mm or more and be normal. Yours is in the smallest range but this may be good news as people with small ducts measured on ultrasound have the smallest risk of stones causing an obstruction there.

The pressure in bile duct and hence its size is dependent upon your own personal physiology, the amount of bile produce the function of a special valve which joins the gall bladder to the duodenum and the possible presence of an obstruction.

Generally speaking the smaller the CBD the less chances of there being Gallstones in the CBD the chances are roughly as follows:
Less than 4mm about 4% chance
4mm-6mm about 10% chance
6mm-8mm about 30% chance
8mm-10mm about 30% chance
Bigger than 10 mm about 50% chance

Gallstones not always show up on ultrasound.

A modest CBD has the ability to expand greatly to pass stones.

I hope this has clarified the situation for you or perhaps it has only prompted more question. The only sure way to find out if you have stones and avoid the surgeon is to try a liver flush. It also provides you with better health as a bonus.

Telman