Buna ziua
I live in Timisoara, the western most city in Romania.
You shouldn't have any worries about visiting or riding here, though I'd advise against riding at night because of the pot holes and the completely unlit horses and carts. I'd agree with others that the standard of driving is generally pretty terrible but you'll be OK if you concentrate.
Road conditions vary tremendously - ranging from wonderful to downright terrible. Unless you've lots of time stick to the main national roads. Everyone's heard of the Transfagarasan (DN7C), and it's certainly worth seeing and doing, but I prefer the TransAlpina (DN67C), which runs more or less parallel the Transfagarasan, about 50 km to the west. Plenty of other cracking roads, and wonderful scenery, as well.
Don't worry about corruption or bent cops - they don't generally hassle foreigners. I've been stopped and fined several times, including a three month ban, and every time they were polite and fair. Watch your speed through the many villages - radar traps are very common.
I wouldn't plan on camping - there are very few campsites but plenty of very cheap guest houses.
Happy to help with route planning. When you say you'll be "passing through", from where to where?
And it will probably be hot. 34 Celsius here today
, and we're only in early June.
Dave