Neither GMAT nor GRE Subject test is required for Fulbright, the only test required for applying for Fulbright is GRE General Test. If you get selected for the scholarship, the committee might then ask you to take these tests depending on your prospective program. If you are aspiring to apply for an MBA on Fulbright, it helps to have great work experience. In fact, the Fulbright explicitly requires at least 3 year experience for business graduates. If you are a computer science or engineering graduate selected for Fulbright, it helps to have some concrete evidence portraying you are a good candidate e.g. research/ relevant work experience. It is only after you are selected that they tell you take GMAT or GRE Subject test.