Trains arrive at Belarus Station from Belarus (Minsk and Brest), Kaliningrad, Smolensk and international destinations including Vilnius, Warsaw, and Berlin. The station is just over 1 km from the Bega Hotel, so if you don't have much luggage, it's quite possible to walk.
By taxi
It should not take more than 10 minutes to drive to the Bega. If you can negotiate a taxi on arrival, the fare should be around $15, but it is probably easier to arrange a transfer with a driver to meet your train, which you can do here.
By metro
Take the metro from Belarusskaya Metro Station one stop north on the dark-green line to Dynamo, which is about 15 minutes' walk from the hotel.