The purpose of this investigation was to study the relationship between sleep quality, problematic smartphone use (PSU) and bedtime procrastination, as well as to assess gender and age differences. A total of 313 participants, aged 18–60 (M = 30 ± 10.1; 53.2% males), completed an online survey between February and May 2023 in Spain. The Pittsburgh Sleep Quality Index, Smartphone Addiction Scale-Short Version and Bedtime Procrastination Scale were used to measure sleep quality, PSU and bedtime procrastination, respectively. Additionally, smartphone use habits were evaluated through self-report questions. Pearson correlations, independent samples t-tests, one-way ANOVA, Bonferroni’s post hoc tests and mediation analysis were conducted. Correlation analysis showed positive associations between the three main variables. Independent sample t-tests indicated females were more prone to PSU along with higher overall smartphone use. Post hoc analysis of one-way ANOVA exposed age differences between young adults (18–25 years old), adults (26–44 years old) and middle-aged adults (45–60 years old) in PSU and bedtime procrastination. Finally, mediation analysis revealed that PSU had indirect effects on sleep quality through bedtime procrastination, but no direct effects on sleep quality. Therefore, PSU, and especially bedtime procrastination, should be considered as targets in future campaigns or intervention programs to improve sleep quality among the young Spanish population.