So what I am asking is not the total travel distance that the Caravan would travel in a lifetime; instead I am asking how far they would tend to go one-way on a two-way trip and how long that trek would normally take. The Indian ocean trade is not included and I am only speaking of the routes that go from China to east Rome.
I originally wanted to close this as a duplicate of this question, How was security on the Silk Road between China and the West maintained?, because the primary answer answers this question as well:
Few people ever traveled the full length of the Silk Road. The goods were transported by a series of routes and agents. This mode meant that local agents, familiar with terrain, politics, and bandits of their own region, who were better suited for the task, would ensure safe transit.
The above also is a reason why Marco Polo's 13th century traversing of the entire route is so remarkable—we get impressions from the entire route. However, this question here dealt with a much earlier period—namely, the mid-7th century as the time of interest as I liberally interpreted "Justinian" as "Justinian II" as there is very little evidence (as far as I know) for the mid-6th century.
Justinian II's mid-7th century was the high period as specified in Valerie Hansen's 'The Silk Road' that focused on a number of locations between Samarkand and the westernmost Tang outposts. It is my impression from that book, though I read it a while back, that pre-Tang unification and garrisoning of the outlying border which opens to the Taklamakan Desert, the 'Silk Road' as a trade route was essentially inoperable. Tang unification was relevant because they paid their troops in silk which was then traded to caravans that moved between the various oases around the Taklamakan, which can probably be considered the most difficult part of the journey.
Here are the primary locations as set out by Hansen, with Anxi being the gateway to Tang China and Samarkand the gateway to the west:
Approximate routes are drawn onto this map:
The approximate distances are 1000km between Samarkand and Yarkand as well as between Khotan and Kroraina; 600km between Yarkand and Kucha, Kucha and Kroraina, Kroraina and Anxi, and 300km between Turfan and Kroraina and Khotan and Yarkand. Most merchant caravans would probably have trod backwards and forwards between one or two of these places, with very few going the entire way from Samarkand to Anxi:
Undeniably, the Chinese-language materials from Duldur Aqur are limited. Totaling only 208 documents, many of them consisting of a few characters, they touch on a surprising range of activities. The historian who has translated these documents ... summarizes their content: "... absense of identifiable commercial documents. No lists of goods destined to be commercialized. No travel documents like the many travel passes for caravans found near the postal station at Yanshuigou. ..." Yet for all their variety, they do not mention anything that looks like the conventional portrait of the Silk Road trade—no private mercants carrying vast quantities of goods across long distances. Trombert believes that Kucha was a center of commerce, but that the merchants traveling there stayed within the city or outside the oasis—not at Duldur Aqur, which is why no commercial documents survive.
Yet, like Duldur Aqur, the much-better-documented sites along the Silk Road also lack documents about long-distance trade. ... the Chinese army's demand for horses constitued a major component of that trade. ...
The surviving evidence from Kucha, as partial as it is, suggests an alternative to the standard picture of the fabled Silk Road trade: rather than a long-distance trade initiated and staffed by private merchants, these materials indicate that the Chinese military contributed significantly to the Silk Road economy. When Chinese armies were stationed in Central Asia, money—in the form of coins, grain, and cloth—flowed into the region. When the Chinese troops withdrew, small-scale trade resumed, largely maintained by local travelers and peddlers. ... Few individuals traversed all of Central Asia, covering the distance of some 2,000 miles (3,600 kilometers) between Samarkand and Chang'an. ...
–Hansen, 'The Silk Road'
Hence Taizong's campaigns are quite relevant, including the garrisoning of the same desert outposts.
Trade to the east of Anxi would have been heavily governed by Tang officials by issuing travel passes and only permitting a limited number of foreign caravans into the interior of the country.
Trade to the west of Samarkand would have been subject to the various powers that governed the area. It seems that the Eastern Romans were able to engage in at least a limited amount of direct trade with the area, but mostly this would have been subject to local rulers' whims.