Background: This study aimed to investigate the association between body composition (BC) specific parameters such as fat mass (FM) and lean body mass (LBM) and bone quality in obese and non-obese young Slovak adults (18–30 years) using bioelectrical impedance analysis and quantitative ultrasound while considering the factors of sex and obesity status; Methods: BC was evaluated using bioelectrical impedance analysis (InBody 770) and bone quality by the speed of sound (SOS) in radius using QUS (Sunlight MiniOmni) in 774 young Slovak young adults aged 18–30 years, categorized by sex and obesity status (body fat %, PBF, ≥28% for men and ≥20% for women); Results: In non-obese individuals, radial SOS correlated positively with FM parameters. Significant positive correlations with LBM, including skeletal muscle mass (SMM), were observed in non-obese men but not in women. Conversely, SOS correlated negatively with FM parameters in obese individuals, significantly only in women. The correlation of SOS with LBM in obese individuals was insignificant in both sexes. Age, visceral FM, FM in the arm, and vitamin D intake were identified as the main predictors of radial SOS in young adults, except in obese men. Conclusions: Findings indicate FM benefits bone tissue in non-obese individuals, while excessive adiposity deteriorates bone quality in obese individuals, necessitating tailored evaluations and interventions based on sex, obesity status, and specific predictors.