There are multiple potential causes. This is a complicated topic, so if no need to develop a detailed understanding you will have to read lots of papers and ideally engage with some experts. Much of the science is relatively new and still emerging, so please be aware that conventional medical lore and many textbooks will not be up to date. Bile acids are cleared from blood by the liver and this involves both uptake and efflux transporters on the hepatocyte plasma membrane. The Bile Salt Export pump (BSEP) is the key efflux transporter and its activity in humans can be impaired due to genetic deficiencies or inhibition by chemicals The inhibitory chemicals includes many different pharmaceuticals and this is one of a number of ways that some drugs are now believed to initiate human liver injury. Entry of bile acids into hepatocytes is mediated by uptake carriers and in principle inhibition of these (NTCP primarily; OATPs also contribute though) can cause elevated serum bile acids too. Although I don't know of any compounds that inhibit these carriers without also affecting activities of other hepatocyte transporters. Blockage of bile flow by obstruction of the bile duct can also be an important cause. Finally, marked loss of hepatocyte function caused by liver cell injury (i.e. liver damage caused in other ways) will impair the bile acid excretion process "secondarily".
Thanks Gerry Kenna for passing through. I know this question in very complicated, because there is no SINGLE pathway that could be thought as the one fully responsible. I asked this question hoping to find a logical explanation of my own results, because all the possible ways that led to TBA elevation came to a dead end with me.