Differential response of bread wheat seedlings from different crosses to contrasting water regimes can be used to point to drought tolerance traits. The aims of this research were to assess: i) assessment of variability and correlations of root system architecture (RSA) traits and stem traits of the parents, chosen from a previously screened collection of 101 wheat genotypes for drought tolerance, and their F1 progeny, in the seedling stage under contrasting water regimes; ii) analysis of associations of the stress indices and RSA and stem traits under induced drought stress; iii) determination of combinations of parental genotypes with the best heterotic progeny, with better early growth of roots and stems and tolerance to drought. Seedlings were grown in hydroponic cultivation conditions under polyethylene glycol (PEG) induced drought stress vs. controlled conditions under completely randomized design with three replicates. The traits measured were: primary root length (PRL), distance to the first branch on the primary root (DFBR), number of seminal roots (NSR), total seminal root length (TSRL), angle of seminal roots (ASR), stem length (SL), root dry mass (RDM), stem dry mass (SDM), and the ratio of root dry mass to stem dry mass (RDM/SDM). Drought stress led to a decrease in the mean values of all root and stem traits by 11% on average, except for RDM/SDM which was increased. The most sensitive trait to drought stress was DFBR (25% reduction), causing root systems to branch at a shallower depth. In conditions of induced drought stress, the strongest statistically significant correlations were found between RDM and RDM/SDM (r = 0.794), SL and ASR (r = 0.708), RDM and TSRL (r = 0.673). The stress tolerance index had the strongest positive correlation with the SDM, PRL, TSRL, SL, and the stress susceptibility index with the NSR. The highest heterosis mean value was observed for PRL (24.6%) and for SL (15.6%) under drought stress. The different directions of average heterosis in induced drought stress vs. control conditions were observed for DFBR, RDM, and SDM, indicating differential traits to account for when planning breeding bread wheat for drought tolerance.