Is it obligatory to perform ablution before ghusl for someone who entered the bathroom while already having ablution?

Wudu is not obligatory before bathing. Rather, it is sunnah (recommended) before ghusl (ritual bath) for janabah (state of major ritual impurity). Wudu only becomes obligatory when performing acts that require ritual purity, such as prayer, touching the Qur'an, and circumambulating the Kaaba.