Does the Bible encourage an engaged couple to travel together to places abroad, so that the lady can meet his family, as they reside in different countries? They still don't belong to each other and temptations are more likely to arise, even in just being boyfriend and girlfriend. Would it be safe to travel with someone who is still a stranger, and the lady does not have any relatives there? Is traveling considered a necessary element of love that one should get close to each other before marriage and share their weaknesses and secrets?
It would depend on the precautions you are taking. There is no requirement for a man's future wife or a woman's future husband to meet each others families. However, it is a sensible thing to do since each are going to have to deal with the others family.
Because the time of marriage is more certain, temptation can increase. "Therefore let him who thinks he stands take heed lest he fall" (I Corinthians 10:12). If you are traveling where the two of you must stay overnight somewhere, make sure she has a companion to join her. If she is staying with your family, it is best for her to stay in another home and join you during the day. Or for her to stay in a different part of the home from you.
I almost gather that you and she have not spent time together, even though you are engaged. Is this an arranged marriage?
This is a must condition that approval is given by the father of the lady before an engagement is done, so involvement of family is necessary in their Asian society. Even Christian couple hung out together a lot, but hers is a conservative family. They said it is not necessary, and they see no valid reason behind spending time together. They think the more you dig about each other the more trouble it will create, make you confuse regarding one's personality, and in doing so many men just dumped their girlfriends, even she have feelings for him, as usually they are the decision makers. Shaking hands with opposite sex is also not consider as an acceptable act in her family. Any suggestion to handle the case?
I'm trying to figure out how you even became aware of this young woman, let alone come to conclusion that you might be interested in marrying her. I assume that your parents arranged this potential marriage? I hope they found a good woman who shares your values.
If this arrangement is not acceptable to you, then call off the wedding and be prepared to find a wife on your own. I feel sorry for the young lady. But can this marriage work? Yes, it will take a lot of effort on the part of both of you because you will have to spend the early days of your marriage learning who you married as well as learning to get along with each other.