There are buses available from Mathura railway station to Barsana via Govardhan. Once you reach Govardhan walk further for 100 meters to catch another bus for Barsana. There are also a 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 (Chhata, National Highway 2) > Barsana. This is the better route due to less traffic and better road conditions and no change of bus and most importantly it saves time but bus services few.