Carolyn,
I've got not very pleasant experience travelling with the train to Bucharest. Yes, it was in December 2006, so many things must have changed in the meantine for the better.

http://patepis.com/?p=192 - this is the story of my travel there. 

Some advice from me:
- Try to use the Romanian train from/to Sofia, not the Bulgarian one
- A better/cheaper option is the bus to Ruse and then the bus to Bucharest. When I travelled, the train spent totally 2 hours waiting at the border.

Please, check with someone that has travelled soon. My information is 4 years old.