Is taking a bus from Warsaw to Elk is a better options?
I don't know.
from Warsaw Central Train Station to Warsaw Wschodnia Train Station?
First of all, there's a chance that your train stops at Warsaw Wschodnia too. Most long-distance trains stop at Warsaw Wschodnia/Centralna/Zachodnia.
If not, then the easiest way is to walk from Centralna to Warszawa Śródmieście (200 meters walk, underground - you exit the Centralna train station directly from the platform where your train arrives - don't go upstairs to the main hall; then choose the correct platform of the Śródmieście station - there should be signs - "kierunek Warszawa Wschodnia" and "kierunek Warszawa Zachodnia").
From Warszawa Śródmieście there's a train every 5-10 minutes in both directions - west and east (you have to buy a ticket).
I assume you'll be arriving in the daytime, because in the night there are few trains from Śródmieście, if any, and going those 200 meters underground can be dangerous too :(