According to Vasmer, нету and нет both originated from Old Russian нѣту and нѣтъ from the older не ѥ тъ, не ѥ ту.
тъ and ту are sg. acc. from improper pronouns тъ and та (in modern Russian тот and та)
Originally both words meant "there is no" (with respect to gender), however, later the gender distinction was lost, and yet later the latter also has come to mean "not" (along with the old meaning) and the former became colloquial.
Нету can only mean "there is no":
― Всё. Больше никаких вещей нету. ― Спасибо, ― сказал Андрей, убирая письмо в карман. [Виктор Пелевин. Желтая стрела (1993)]
As with other colloquial but not rude words, it's OK to use this word in informal speech.
This word is considered a little bit childish though, so it's OK to answer your boss нету in a private informal conversation but not on an official meeting or in business communication.