You have it backwards. The plague starts in east Asia, then spreads West along the Silk Road, it arrives at the Black Sea, and then is carried to Venice. Most likely it was in rats that were on the ships which the merchants of Venice operated in the Black Sea. It arrives in Venice in 1347, and the next 36 months are the event that in the West is called The Black Death.
This was the 1346-53 epidemic.
The earlier black death epidemic starting at 541 (https://en.wikipedia.org/wiki/Plague_of_Justinian) was a bit more influental, and killed about 40% of the population. This came from Egypt to Europe.
But recent genetic studies also suggest it came from China instead, same as the later plagues.
