According to TriMet system map that I picked up today, the following routes go by Union Station:
14,35,44,54,56,58,and rush hour are 31,32,96.
From the Old Town/Chinatown MAX stop, Union Station is 5 blocks West, then 5 blocks North. Just a couple blocks from the Greyhound Terminal.
I think it may be faster to walk this distance then take MAX downtown then bus to Union Station.