Modern Non-Orthogonal Multiple Access (NOMA) and Unmanned Aerial Vehicles (UAVs) wireless technologies are valuable assets in emergency scenarios to enable quick and flexible infrastructure of wireless communication networks. Still, efficient trajectory planning of UAV-NOMA emergency networks is a big challenge where the UAV should assist the maximum number of survivors and optimize its limited battery energy. Hence, in this paper, we formulate this problem as Budgeted Thompson Sampling for UAV Trajectory Planning (BTS-UTP), which is a theoretically guaranteed Budgeted Multi-Armed Bandits (BMAB) derived from the original TS via considering the random cost for drawing an arm and the total cost is constrained by budget (UAV energy). Here the bandit player, arms, cost, and payoff are the UAV, disaster area grids, UAV battery expenditure, and the number of assisted survivors. Numerical results ensure the superior performance of the proposed BTS-UTP technique.