Hi Mark,
Your bilirubin level is higher than normal for someone without thal minor, but not unusual for thal minor. Anything lower than 6 is considered to be mildly elevated, and it is not an indication of liver disease. With thal minor, some of the red blood cells are not normally shaped and are destroyed by the body at a higher rate. This is called hemolysis and is common in thal minor. If you are ever told that your spleen is enlarged, this is also the result of hemolysis. Even though a bilirubin level of 2 or higher can cause jaundice, it is not a serious problem. However, long term this can lead to gallstones.
To lessen the hemolysis, keep your good diet, avoid processed foods and make sure your diet is high in antioxidants. Take folic acid daily. 2-5 mg per day. This helps to build healthier red blood cells that last longer. I also suggest vitamin E, B Complex and magnesium, which all have roles in red cell production and health. Vitamin C also plays a big role in circulatory health, but supplementing may not be needed if you get enough vitamin C containing foods daily. If you bruise easily, take vitamin C supplements. Not only does your body need nutrients to produce red blood cells, but hemolysis depletes nutrients, often beyond what is possible to replace solely through diet.
There is no reason to assume any serious illness. Hepatitis would give you a much higher bilirubin level. Your level is consistent with the hemolysis of thal minor. Start folic acid today. Your body needs a constant supply because your production of red cells is overactive, as your bone marrow tries to compensate for the low hemoglobin level that is the result of not enough good red cells being produced. This added activity is fairly futile, as more bad red cells are produced. Take a look at threads in the Diet, Nutrition and Supplements board. You will find many posts about what people do to improve their health when dealing with thal minor.