sorry for the delay in the sources; work, work, work.
Cathedral, Forge & Waterwheel by Frances & Joseph Gies- a general discussion in the introduction deals with the transfer of technology between China and Europe (Greeks and Romans) from Ancient times, with the role of Persia and Parthia and India discussed. a chapter on clocks, of all things, also makes mention of scholarly exchanges between the West and China on astronomical matters, with the spread of years including Rome, but whether Rome was in fact the source of this exchange is not mentioned.
The History of the Ancient World by Susan Wise Bauer- numerous references to various exchanges between Roma and Persia and Parthia on the one side and India and China on the other. Most of the information cited on the exchanges between India and Persia and Parthia are based on archeological finds and supposition. she also gives several references to a number of planned expeditions from both Rome and China, but fails to mention if any even started much less made it. She does, however, detail the military efforts of various Chinese emperors to protect the trade routes as far west as their military power allowed. this would suggest that trade, at least, between the East and West had become important to China.
There is a periodical in Australia called Quadrant that deals with a number of issues but also includes some preliminary historical works by Australian scholars- mostly thoughts in an early stage of development. I can not find the issue i was looking for but it was definitely from 2006 and it discussed the fact that the West and China both had access to works by Aristotle but apparently not by Zeno/ Xeno in thier original Ancient Greek- possibly a legacy of Alexander in India/ Afghanistan. (Bauer suggests that earlier Greek mercenaries established the first Indian kingdoms) however recent evidence indicated that a Spanish monk discovered Zeno's work in Latin, but that the Chinese had not translated it. as the only reference came from the monk's personal account (written in the 1800's) it was deemed interesting but not conclusive proof of regular official exchanges between Rome and China.
HAL Fisher and John Julius Norwich both make oblique references to exchanges between the two empires, but this may be nothing more than a "it seems likely that..."