"I am to travel" is never used by itself, or only very rarely. You would almost always give more information and make a modification. For instance: "I'm supposed to travel to that conference next week". As Mike mentions, when you say this the listener will believe there is some form of obligation, duty, or you have no choice. It may only be a 'light' obligation, but some form of obligation is usually implied. So if I said "I'm to travel next week", I am implying in some manner that there is at least a small obligation/requirement that I do it. But this usage isn't that common. It would be far more common to be more explicit and say "I have to travel next week" or "I must travel next week" or "I'm supposed to travel next week" or "I'm going to travel next week" (and give a reason perhaps)

It's used mostly in formal situations, and usually implies an obligation or a command. "All employees are to report to their supervisor." The meaning is similar to "I have to" or "I must" rather than "I get to." In the US it's rarely used in conversation, but I would say it's a little more common in the negative form. "You are not to tell anyone what I told you."