I think this question is a really difficult one to answer given the myriad of forces involved in why aspects of international culture were/were not adopted in the Middle Ages (guessing that is the timeframe for this question based on "Silk Road" references). There were undoubtedly social reasons, religious reasons, economic reasons, and political reasons for this. I'm not expert in the field by any means, but hopefully this can help provide a point of entry!

To start, Christianity needed to "fit in the mold," so to speak. In the 2nd and 3rd century AD, Christianity was still in its infancy; the New Testament hadn't come to full fruition and there were still intellectual challenges facing the religion. Such intellectual criticisms needed to be addressed and reconciled. Clement of Alexandria used philosophy to show similarity and integration of the Christian philosophy with other philosophies already in play. In his Exhorations, he shows off his awareness of Greek history and religion while simultaneously espousing the falseness of it, saying how only through Christ can one fully participate in Logos. Thus we see how ideas and stories shift to fit into the emerging Christian doctrine. This pattern of integrating is important to keep in mind, I think!

In pre-Medieval times, the first Christian notice of Buddhism that I'm aware of is with Clement of Alexandria in 212AD. In his Stromata (ie, Miscellanies), he recognizes some Indians who obey the precepts of Boutta, "whom on the account of his extraordinary sanctity they have raised to divine honours." Clement spoke highly of Buddhism, calling it a philosophy "first in its ranks" for shedding light over the nations." He likely had access to Buddhist texts thanks to Ashoka's command to spread the dharma amongst Greek rulers in the 3rd century BC (Rock Edict XII). It wouldn't be far fetched for him to see similarities between the Buddhist "prajna" (roughly "wisdom" or "insight") and the Greek "sophia" (also, roughly "wisdom" or "insight into the true nature of reality") given the esoteric meanings of the words and their presence in cosmopolitan Alexandria.

Finding that similarity would be important in spreading Christian doctrine rather than having Buddhism overpower it, if Buddhism was trying to achieve that goal. But Buddhism really didn't spread past the Middle East in those earlier days. The Turkharistan and Sogdiana regions in the Mid East acted as major trading hubs on the Silk Road between the four directions. All cultures religions and philosophies aggregated there in the 1st century AD. Diversity existed in part because the various city-states of the region were not part of a single polity nor did they tend to have complete control over their subjects. Thus no one single religion/philosophy/politic/etc could exert dominance. It should also be noted that this lack of cohesion resulted in differing rituals even among practitioners of the same religion; Zoroastrians and Buddhists in Sogdian cities practiced differently than those in Iran, for example. Locality plays a major role in evolution of religion, philosophy, and other cultural aspects after all.

I point this out to show the kind of "freeflow" exchange of ideas and ritual without an overarching force pushing for unity. This fits in with the spread of Christianity by making use of or changing local ritual. We find this a lot with the Nestorian Christians in the 7th/8th centuries as we see Alopen (the first Christian missionary to China that I'm aware of) start aligning the Buddhas with angels, saying how the Buddhas can know the Lord of Heaven while humans cannot, how returning to the Buddha requires comprehension of one's sins and wicked deeds, etc, etc (from the Jesus Messiah Sutras).

But then we come to the rise of Islam. The conquest of the Arabs and Islam was pretty complete in the Middle East, including the Turkharistan and Sogdiana regions. After being conquered, the people were willing to abandon their religions and convert to Islam as long as they received the benefits of doing so; Arab governor Ashras offered freedom from taxation for converts who underwent circumcision and read a section from the Koran. The "spread" of Eastern philosophies kind of dies at that point in history. It's seen that after the conquest, even the intellectual side of the Arab world spread teachings of the West, not the East, as the works of Aristotle, Plato, and others covering subjects like governance, mathematics, etc became popular. Those were topics to build up a civilization socially and economically.

It should also be pointed out that Tang Wuzong in the 9th century purged all non-native Chinese religions from the state, including Buddhism, Zoroastrianism, Manichaeism, and Nestorian Christianity. Confucianism and Daoism remained. Not to mention the Tang lost control of their western lands in the An Lushan rebellion in the 760's, closing off the Silk Road at the time. All this affects the spreading of East/West religions/philosophies during this timeframe.

So now we have a closed Silk Road and an Islamic faction seeking dominance. The threat to Christianity was enough to overshadow any super, super small delegation of Asian religions during the early Medieval Ages. The Mongol invasions and conquering of China helped a bit due to their reopening of trade routes. We see accounts of travel and settlement of Westerners in the Asian region- such as Marco Polo. Kollam in India and Yangzhou in China become hubs with bishops like John of Montecorvino spreading the faith and aiding fellow Christians under the Mongol reign.

However, given that awareness, supposedly there are about 12 accounts surviving from 1244 to 1349 detailing Western encounters with travelers from the East. The East became virtually shut off from the West thanks to Islam, the An Lushan rebellions, then the fall of the Yuan Dynasty (ie, the Khans), Black Death, etc. Accounts from Montecorvino find the Asian religions to be idolatrous sects and engaged in blasphemous ritual. This no doubt shaped perception in Europe at the time, possibly creating a stigma that ever kept the religions or philosophies from really taking hold. Then again, it could be argued that during the Medieval Ages, Western religion didn't really take hold in the Asian region either at the time due to the geographical distance and all the events leading up to it (a lot happened to kill/persecute/convert)! After the 1500's, I think things change, but that's a different discussion.

I should point out that the academic sources on this topic of Buddhism in Medieval Europe is fairly sparse, from my understanding. The ideas I present above are based on sources (given below) but also general thoughts on how transmission/cultural integration works. Some more recent studies claim that nothing of Buddhism or Eastern philosophies were known to pre-1250 Western civilization other than the name of the Buddha via Manichaeism texts, thus drawing the conclusion that the Jewish/Christian/Islamic west associated Buddha with Mani, Zoroaster and the like.

Sources-

Christian Responses to Buddhism in Pre-Medieval Times (1985) - David Scott - JSTOR A Silk Road Legacy: The Spread of Buddhism and Islam (2011) - Xingru Liu - JSTOR Stromata, or Miscellanies - Clement of Alexandria Exhorations of the Greeks - Clement of Alexandria Random sources related to Chinese history Random memories on Zoroastrianism Eastern Religions and the West: The Making of an Image (2013) - Nathan Ristuccia - Open Source

The last source, Eastern Religions and the West, is the one which discusses lack of pre-1250 references to Buddhism. The accounts detailed therein are pretty interesting IMO.