Buddhism actually did spread west from its heartland in Eastern India/Nepal to what is now Afghanistan. But once you go further west, you would be in Persia, where the official state religion was Zoroastrianism. Buddhism and other non-Zoroastrian religions were persecuted by the Sasanian empire [1]. After the Islamic conquest of Persia, Buddhism continued to be persecuted, as Buddhism was not at first considered one of the protected religions.

[1] The Cambridge History of Iran

hi! you may be interested in these previous threads

• How did Buddhism spread to Japan and why it didn't spread to Europe?

• Why didn't Buddhism spread west to the Mediterranean like it spread east into China?

• Why didn't Buddhism spread westward towards Europe despite the contact between the Greeks and the Indoiranians after the conquests of Alexander the Great?

• What do we know (if anything) about the buddhists who lived in the Hellenic / Roman world?

• How popular/widespread was Greek Buddhism?

• i have a question regarding Buddhism and Europe

• Why did Buddhism spread East along the Silk Road, but not very far West?

• What were some distinct characteristics of Afghan Buddhism?