Is it permissible to buy a bicycle without the parents' consent, knowing that the desired legitimate interest in buying it is to avoid mixing in buses, facilitate attendance at Islamic scholarly lessons, and maintain kinship ties?

If the parents' prevention of buying a bicycle is without justification due to their fear, then obedience is not obligatory. However, they should be persuaded and placated. But if the fear is justified, such as the child not being skilled at riding, then obedience to them is obligatory, and disobeying them at that time is considered disobedience (عقوق). Disobedience (عقوق) includes disobeying their command or prohibition in matters that cause fear for the child, except in the case of obligatory jihad.