I guess, my lift will help you to get home on time. There is nothing wrong to accept such an honourable offer. Your acceptance can help to build up a lasting relationship.
Both men and women have to accept gifts and lifts, but one needs to study each party very well. Most men only give an offer when they are in love with a lady. This is where the woman has to be smart and deny the offer.
It is a fact that most people do offer for a reason which is bad. Be careful with both offers and gifts.