Is there a reason a TA and a professor may have to travel together?
In most cases, a teaching assistant would not have any reason to travel with their professor, since their responsibilities are around teaching. Perhaps if the class was an expedition for field work in an archaeological department or something (I think I have heard of a department doing this), but then it would have all of the students as well.

A research assistant, on the other hand, will often travel to a conference with their advisor, if they have a paper or poster to present. Thus, to me, the most likely case for a teaching assistant traveling with a professor is if they are also supervised in research by that same professor.