Hi Kamilla ! I am female, spent three weeks alone in Romania, went all around the country, and my conclusion is : where the heck does that bad reputation come from ?
There are problems you may encounter, and for that, read the danger and annoyances section in the Lonely Planet. It tells you everything you need to know, and how to get out of bad situations. But those scams (like pickpockets) are mostly targeted on men.
Trains, this is where you might have problems. Might. Some people are drunk, and trains have closed compartments. So use commun sense if you sense any danger, and change place.
The rest is the same to anywhere on the planet, avoid walking alone at night, look confident, etc.
Beside that, important advise : bring toilet paper for train rides ! You'll soon understand !
And enjoy your time in beautiful Romania !
You can send me a personal message, would you need more answers to your questions.