Is it necessary for me to perform ablution after bathing?

If by bathing you mean ghusl (ritual bath), its complete description includes ten things: the intention (niyyah), saying "Bismillah" (in the name of Allah), washing the hands three times, washing away any impurities, performing wudu (ablution), pouring water over the head three times while running fingers through the roots of the hair, pouring water over the entire body starting with the right side, scrubbing the body, moving from the bathing area to wash the feet, along with the recommendation to run fingers through the roots of the hair and beard.

As for the sufficient (mujzi') description, it involves making sure water covers the entire body, along with rinsing the mouth and nose, and having the intention for both ghusl and wudu. This is sufficient, though it means leaving what is better and more preferable. Scholars have used as evidence for the sufficiency of ghusl over wudu that Allah Almighty enjoined only ghusl upon the person in a state of major ritual impurity (junub), and did not enjoin wudu. And Allah knows best.