Trains to and from Cluj Napoca to the nearest train station to Borsa is in Viseu de Jos. The trains run 3 times a day between Cluj Napoca and Viseu de Jos and is 2-3 hours long, depending on the train and cost aprox. 30 lei (7 euro). You can see the schedule here: www.cfrcalatori.roAfter you arive in Viseu de Jos (30 km far away from Borsa) you can take the buss to Borsa, see the schedule here:www.autogari.ro/Transport/ViseuDeJos-Borsa
The times of the trains vary from year to year so it is best to check the train schedule.
Trains Bucharest – Sighetu Marmatiei or Viseu de Jos
There is a night train with couchette from Bucharest Nord train station to Sighetu Marmatiei which leaves the capital early in the morning ( the times vary so check in advance at the station when you buy the ticket) and arrives in Sighet station also early in the morning. It is a comfortable and cheap connection between the capital of Romania and Maramures. The night train also runs in the opposite direction.
From Sighetu Marmatiei you can take the bus, see thebus section.