I'm most interested in how they traveled during the height of the empire's power (the reigns of the "five good emperors"), but I'm curious about other eras as well.
Additionally, does anyone have any good books to recommend on ancient trade and commerce, and in particular Roman activities outside the empire?
As a follow up, did Roman citizenship carry and weight outside the borders of the empire? If a Roman was in, say, Persia or India would local authorities be reluctant to treat the merchant poorly/demand bribes or something, out of fear that the Romans might do something?
I can't comment on Roman merchants specifically, however, I remember reading about how Muslim merchants protected themselves. First, Muslim (or in some cases, Jewish) merchants would acquire letters of safe conduct from local rulers which would guarantee (at least in theory) their safe passage through territories. Second, Muslim merchants would arrange to be accompanied by a partner, usually another trader, called a rafiq, and each partner would rely on the other for some degree of protection.
I know this doesn't answer your question, but hopefully it can point you in the right direction, or at least, give you an idea on how merchants during the ancient world handled their personal security while abroad.
Bernstein, WJ, A Splendid Exchange: How Trade Shaped the World, 2008, p. 6.