Candle lighting Rav Moshe used to ride in car to yeshiva afterwards.

Igros Moshe (OH I #96) Question Is my traveling in a car after Candle lighting before Shabbos to the yeshiva which is two minutes away. Is this possibly a prohibited activity? Answer I got great pleasure that you made the effort to fulfil the mitzva of admonishing others according to your understanding of the situation and G-d forbid! that I am bothered by it. Furthermore as a response to your question I will no longer travel in a car after candle lighting bli Neder even though there is not the slightest violation of Halacha or Maris HaAyin.  You should know that the prohibition of Maris HaAyin only applies to things  that are typically prohibited but now he is doing it in a manner that is technically permitted nevertheless we prohibit it because of Maris HaAyin . For example to do work with a Goy that many people do by hiring them for a day. Or hanging up wet laundry in a sunny place which results in people suspecting that you washed the  laundry on Shabbos. In contrast if you do something which is well known to be permitted there is no need to be concerned with those few who mistakenly think it is prohibited and it is clearly not prohibited.  The present case where it is known that all women begin Shabbos with candle lighting while the men  wait a little later. Since the time of candle lighting is generally fixed at 20 minutes before sunset (shkiah) . Thus it is well known to most people including the  women that men are still allowed to perform work within the 18 minute period before shkiah even l’chatchila as long as they have not accepted that Shabbos has started.  There are at least 11 minutes after I get in the car until shkiah and during this time melacha is clearly permitted l’chatchila  and there is no question that there is sufficient time to travel to yeshiva before shkiah. Even if there are some women who mistakenly think that it is prohibited to do any melacha after candle lighting even for men it is not relevant to prohibit this car ride because of Maris HaAyin nor should it be of concern. Because the truth is that it is permitted for men who have not accepted Shabbos.  Nevertheless since you write that this might cause a problem for some women and men who mistakenly this that I am violating Shabbos, I will bli Neder will not travel in a car after candle lighting.