What are the likeliest causes for rising indirect bilirubin levels?

It is impossible to make a definite diagnosis based solely on the given data. But there are some likely options which should all be checked. Here are the possibilities and test which should be done to check them:

1. Bilirubin is a product of erythrocyte breakdown. That's why predominantly unconjugated hyperbilirubinemia could be a symptom of hemolysis or dyserythropoiesis which are simple to check. The patient should check their reticulocyte level (which should be high as the bone marrow tries to compensate for the breakdown of erythrocytes), lactate dehydrogenase level (which should be high because it's a product of erythrocyte breakdown, especially if hemolysis in intravascular), haptoglobin level (which should be low because of an increase of free hemoglobin which binds to haptoglobin). The patient should also check their hemoglobin level which should be elevated in case of intravascular hemolysis, but will be normal if hemolysis is extravascular. If any of the mentioned substances aren't within normal range, peripheral blood smear test should be further made to check for abnormalities of red blood cells. (Hemolytic Anemia: Evaluation and Differential Diagnosis)
2. Any type of viral hepatitis could be the reason for elevated bilirubin. Viral markers should be checked. (Wikipedia - Hyperbilirubinemia)
3. Any biliary stricture can cause a moderate rise in bilirubin level. This includes gallstones, benign and malignant tumors (pancreatic adenocarcinoma or cholangiocarcinoma). Portosystemic shunt could also cause elevated indirect bilirubin because some amount of blood with indirect bilirubin would bypass the liver and the process of conjugation. (Wikipedia - Hyperbilirubinemia) Both of these conditions can be seen with ultrasonography. However, these conditions are not likely because biliary strictures predominantly cause conjugated hyperbilirubinemia. (Biliary strictures: diagnostic considerations and approach) Still, they should be checked because these conditions are very serious.
4. The patient should be asked about their history of drug use. Some medications, such as gemfibrozil, irinotecan and the protease inhibitors, atazanavir, and indinavir, can elevate the level of unconjugated bilirubin because they reduce the hepatic uptake of it. (Evaluating Elevated Bilirubin Levels in Asymptomatic Adults) The patient should also be asked whether they have had any surgeries or suffered any traumas lately which could cause hematoma which is connected to erythrocyte breakdown and consequently a rise in unconjugated bilirubin.
5. If all of previous conditions don't exist then we can suppose that the patient has either Gilbert's or syndrome or Crigler-Najjar syndrome. If indirect bilirubin continues to rise and rises above 85 micromole/litre we can suppose that the patient has Crigler-Najjar syndrome and if the value is lower than 85 micromole/litre we can suppose that the patient has Gilbert's syndrome. Both of the syndromes are mostly harmless in adults. Potential jaundice can be treated with phenobarbital. Both syndromes can be definitely proven with genetic tests. (Evaluating Elevated Bilirubin Levels in Asymptomatic Adults)

If there are some other possible causes which I missed, please write another answer or let me know in the comments.