As an unashamed train-spotter I had to look this journey up just for fun. My first stop is always the excellent Seat 61 website.

Here's the interesting bit:
'To book the Bucharest to Chişinău train, either buy tickets at the international booking office at Bucharest Nord station as there are almost always plenty of places available even on the day, or e-mail the Wasteels office in Bucharest on [email protected] or via their website www.triptkts.ro. Their service has been reported as 'absolutely first class', and you can pick up the tickets in Bucharest. They have an office at Bucharest Nord railway station. Alternatively, telephone +40 21 300 2730 or +40 21 300 2731.

The Bucharest-Chişinău train cannot be booked online, nor can it be booked through the normal computer reservation systems used by western European railways and ticketing agencies.'

http://www.seat61.com/Moldova.htm#.VZECskao0sQ

Let us know how you fare!