Kursk Station is the Moscow terminal for trains to/from central Russia (Kursk and Nizhny Novgorod), eastern Ukraine (Donetsk and Kharkiv), and some Sapsan high-speed services from St. Petersburg. It is just over 2km from the Ulanskaya Hotel.
By taxi
The drive to the Ulanskaya Hotel from the station will take around ten minutes in reasonable traffic. Taxis should cost $15-20, or to save trouble you can book a transfer with driver to meet your train here.
By metro
From Chkalovskaya Metro Station (connected to the mainline station concourse) travel north on the pale-green line one stop to Sretenskiy Bulvar, which is about 250 m from the Ulanskaya Hotel.