Please advise if it is permissible to travel with a non-mahram female /male to work.

Answer

It is haraam to travel with a ghair mahram to work or to be with him/ her. It is not permissible to even work with non-mahram males/females. Contact with them is in violation of Islam's Hijaab rules. Such contact inevitably leads to zina of various kinds. Even if the ultimate act of zina is not committed, zina of the eyes, of the tongue, of the ears and of mind must incumbently take place when there is free contact with ghair mahrams.

Every Muslim is bound to incumbently follow the Shariah. We all falter, stumble, fall and commit sins. But commission of sin should not lead to justification of sin. While the former is fisq, the latter is kufr. Iblees justified his sin and in consequence became a kaafir, everlastingly accursed and rejected. On the other hand, Aadam (alayhis salaam) regretted his error, shed tears in profusion and repented sincerely. In consequence of his humility and acknowledgement of his error, he became elevated and closer to Allah Ta'ala than the rank he had held in Jannat prior to his error.