How do gallstones cause bile to build up?

Bile is produced in the Gallbladder, so if a stone is stuck in the cystic duct it prevents the bile from leaving the Gall bladder. If that happens then bile will continue to collect in the GB with nowhere for it to go, therefore increasing the size/pressure of the GB itself. Hope this helps

But how can bile continue to accumulate in the gallbladder if the cystic duct is blocked?

Bile is not produced in the gallbladder, it is produced in the liver. The liver then releases the bile into the gallbladder to be stored. When bile is needed it is released through the duodenum into the small intestine this is where the bile passes through the cyst ducts where they may be lodged into the ducts as well as the common bile duct, or the ampulla of Vater. If there is blockage of this then bile doesn't get to the small intestine and it is then accumulated in the gallbladder thus increasing pressure. You can see the connection with the picture I have attached. It doesn't show the connection of the liver to the gallbladder though.

Does this help you, or are you still confused? If you are I could explain it in some more detail.