I am a married man and an unmarried woman. Does traveling mean that she likes me?

Not exactly. Some women are simply fooling around and hooking up everywhere. Seeing that you are not ready to take the bait is their goal for married rich men. I don't have to marry you. I relax myself and my vanity is satisfied. So, don't worry too much. If you want to relax, just play together for two days, have an affair and find out if you can bear the consequences.