I might be misunderstanding you, but I think there's a flaw in the idea behind the question: although what we call now "the silk road" was a vast web of comercial routes encompassing much of Eurasia, most, if not all, commerce done throu it was local; goods usually changed hands many times from origin to destination, so very few people would travel the whole distance between, say, Rome and China; and if someone did they wouldn't be merchants, probably, but adventurers, historians or diplomats. So, basically, if you were a silk road merchant your route would be more or less local, ascribed to polities, areas and roads you were familiar with.

Given that as a start, the answer to your question is "it depends". Mainly on the area you were working: if you were based on the deserts of Central Asia or Arabia your picture of lonely caravans looking for the next oasis wouldn't be that innacurate, but it would be pretty exceptional. Just think the silk road created huge cities along its way, so there would be a greater numerical chance of you focusing on some mayor comercial hug like Merv or Constantinople; in that case, you would be traveling densely populated, and military active, areas, sharing the road with a lot of people. Furthermore, goods coming from the route got to exotic, far away places, like Scandinavia, or central Europe: Venice originally got all its money trading pepper, one of the staples of "silk road" trading goods; so if we become a bit flexible, entering the venetian lagoon heading for Saint Marks was technically the silk road. You would see quite some people when doing that. Furthermore, you would be seeing "your" people as, as I said earlier, trade along the route consisted on goods changing hands locally, a number of times, untill it reached the destination. In that regard, trading on silk route goods wasn't very dissimilar to any other kind of trading, at least in terms of "you being a regular silk road merchant".

Short answer: your job would be more like a contemporary truck driver going back and forth than a Marco Polo thing, although covering shorter distances. Depending on the stretch of the route a given merchant was working, he/she would probably travel trough some of the most densely populated areas of the time,althou there where clear and key exceptions, mainly deserts.

I hope this non answer satisfies you, I'll be more than happy to answer further questions. There are some first hand writings on exceptional, full length silk road traveling apart from Marco Polo. If you want a (very) boring but realistic account you can look for a translation of "Embajada a Tamerlán" by Ruy González de Clavijo, a XV Castilian diplomat who travelled to Samarkand; Wikipedia says it was translated as "Narrative of the Embassy of Ruy Gonzalez de Clavijo to the Court of Timour at Samarcand AD 1403-6)".

Edits: Personal Crusade against my self correcting cellphone keyboard,plus Clavijo wrote in the XV Century, not the XIV.