Ibn Baz: we do not have men with us in the car

Q 6: We are a large family, having a chauffeur who drives us to schools, markets, and visit to our relatives. What is the ruling on our going, we are females, with him inside and outside the town, given that we do not have men with us in the car? 

A: There is no harm in this, if there are two or more females as long as there is no cause of suspicion. There is nothing wrong with going with him to the school or elsewhere. If it is possible to have a man with you, this will be much better, but this is not a must. The Khulwah (being alone with a member of the opposite sex) could be avoided just by having another woman or man, along with having no cause for suspicion, since it is not possible to always have a Mahram (spouse or unmarriageable relative) available. However, if the distance is too far or a woman is going to travel, she is not permitted to travel without a Mahram. The Prophet (peace be upon him) said: A woman should not travel except with a Dhu­Mahram (spouse or unmarriageable relative). (Agreed upon by Imams Al­Bukhari and Muslim) 

It is also necessary to wear Hijab (veil) and beware of the causes of temptation to avoid any harm expected.