I noticed that there are a lot of walk in facilities that conduct ultrasounds for pregnant women without referrals for an out of pocket price. Where can I go to get this same type of thing for an abdominal ultrasound of the liver and bile ducts?

You will likely. need a physician's order,but most places will take cash.It can become a negotiation.
I don't. know of any. I suspect many of those facilities you mention are performing nondiagnostic ultrasounds for women who want 3D pictures of their baby. If you have pain or other symptoms, it is not a good idea to try to diagnose and treat yourself. See your doctor, explain your symptoms, and get appropriate management.
Different . There is very little training necessary to just take photo studio like baby pictures of a fetus.A medical ultrasound of a fetus or any thing else requires a great deal of training and expertise to know what u r looking for and how to show it.U also need expertise in order to interpret the images. I know of no facilities with this type of trained personnel that don't require a doctor's order.
Stop by. I would stop by these same clinics and ask if they can do an abdominal ultrasound. They may be happy to do that. The technique and equipment are basically the same. Good luck. (They may require that you furnish a name of a doctor to whom you can follow up.)