Bullying has been seen as a public health issue given to the fact that it causes psychosocial and academic problems in thousands of children worldwide. This study investigated how perceived parental responsiveness and neuroticism predict bullying behaviour among in-school adolescents in Ibadan, Oyo state. A Cross-sectional research design, involving a purposively sampled 428 participants from both private and public secondary schools whose mean age of 15.06 ± 1.52 years was utilized. A 37-item self-report questionnaire comprising socio-demographics, perceived parental responsiveness (α = .93), neuroticism (α = .62), and bullying behaviour (α = .86) was administered. Four hypotheses were tested using multiple regression, t-test of independence and One-way ANOVA, at 0.05 level of significance. Results showed that Perceived parental responsiveness and neuroticism jointly predicted bullying behaviour [F(2,363) = 56.40, R = .49, R2 = .24, p < .001]. Independently, perceived parental responsiveness (β = − .46; t = -8.89; P < .001) and neuroticism (β = .14; t = 2.92; P < .05) significantly predicted bullying behaviour. Results further revealed that male adolescents (= 13.12) reported significantly higher bullying behaviour than female adolescents (= 10.31). Furthermore, the result revealed a significant difference in the mean score of parental marital status on bullying behaviours [F (4, 422) = 4.41; P < .01]. It was discovered that adolescents whose parents are divorced (x̅ = 19.73) reported higher bullying behaviour. More so, the result shows that bullying is higher in private schools than in public schools. Conclusively, bullying behaviour differs by gender, type of school, level of parental responsiveness, neuroticism and marital status of their parent.