There are buses available from Mathura railway station for Barsana via Govardhan. Once you reach Govardhan walk further for 100 meters to catch another bus for Barsana. There are also few autos available from Govardhan to Barsana.
Mathura railway station > Govardhan – approx. 20 km – bus fare Rs. 20/person
Govardhan > Barsana – approx. 20 km – bus fare Rs. 20/person
The above said is the most common bus route but there are few buses that follow another route i.e., Mathura station > Barsana More (Chata, National Highway 2) > Barsana. This is the better route due to less traffic and better road condition and no change of bus and most important it save time but bus services few.