Trees in dense urban environments are often planted in bioretention cells with an underlying trench (BC-T) providing both stormwater pretreatment and storage. The BC-T design is based on a water balance; however, some input data (tree water uptake and water-holding capacities of soil filter and trench substrate) are difficult to obtain. The goals of this paper were (i) to study the sensitivity of such data in the BC-T design (i.e., their effect on the size of the drained area which may be connected to the tree pit), and (ii) to recommend a possible simplification of the water balance for engineering practice. Global sensitivity analysis was performed for the setup of a BC-T used in Prague, Czech Republic, assuming three different trench exfiltration rates. The most sensitive variable affecting the size of the drained area is the available water-holding capacity in the trench. The simplification of the water balance is highly dependent on exfiltration conditions. At high exfiltration rates (18 mm·h−1 and more) or for a trench with an underdrain, the water-holding capacity in the soil filter and the tree water uptake can be omitted; whereas, at low trench exfiltration rates (1.8 mm·h−1, without an underdrain), both the water-holding capacity of the trench substrate and the potential tree water uptake have a significant influence and cannot be omitted.