There is a broad consensus accepting that psychological variables such as stress, anxiety, or depression play an important role in bruxism. The COVID-19 pandemic has led to an increase in stress, anxiety, and depression levels. The purpose of this study was to evaluate the impact of the COVID-19 pandemic on possible awake and sleep bruxism prevalence and on the psychological factors associated with bruxism, comparing pre-pandemic, pandemic/lockdown, and post-pandemic samples of first-year students. A total of 274 dentistry students from the Complutense University of Madrid participated in the study: 92 from 2018/2019 (pre-pandemic), 90 from 2020/2021 (pandemic), and 92 students from 2021/2022 (post-pandemic) academic years. The participants filled out a thorough battery of validated questionnaires evaluating bruxism and different psychological characteristics, such as anxiety, depression, somatization, personality, and stress coping styles. While sleep bruxism prevalence was significantly higher for the pandemic group, awake bruxism was smaller in comparison to pre-pandemic and post-pandemic groups. The post-pandemic group also presented higher levels of neuroticism and agreeableness personality traits, and positive reappraisal than the pre-pandemic group, with the pandemic group somewhere in between. Additionally, both the pandemic and post-pandemic group showed higher levels of depression and acceptance/resignation coping styles than the pre-pandemic group. Thus, among the three groups of students, the post-pandemic group was the one that showed a larger effect of the pandemic situation in their psychological variables, presenting higher levels of anxiety (state and trait), depression, acceptation/resignation coping style, higher neuroticism (emotional instability trait), and lower agreeableness trait. Nonetheless, the increase of positive reappraisal in the post-pandemic group (an adaptive coping stress style) might be also a sign of recovery. The higher sleep bruxism for the pandemic group might be related to the pandemic situation and lockdown, passively suffered, possibly promoting feelings of impotency, increased levels of depression and acceptance/resignation (normally considered a passive/maladaptive coping style), while acute stressful situations derived from daily personal social interactions might have increased anxiety levels and induced higher levels of awake bruxism observed in both the pre-pandemic and post-pandemic groups. However, further research, including larger and more representative samples, is needed to confirm this possible relationship.