Rome traded with India in a VERY MASSIVE way. They transported their wares to very BIG cities in the Red Sea, Egypt. Those cities were the equivalent of modern day Hong Kong, from there it was possible to reach India in days. The cities were monumental, but nowdays are dust.
Rome never had direct access with China, the first westerners that the Chinese saw were a legion of Roman soldier from Galia, they were captured by the Partians (the descendants of the Persian empire) and sent to the Chinese emperor as a gift. They provoked a conmotion since they had never seen westeners.