Don't know to what extent I can help you... but having been to Bucharest three times in the last three years I think I'll give it a try!
The reason I'm not so sure if I can really help is that I never visited Bucharest independently - twice I stayed with friends, once I was at a conference (at the very nice Marriott) but again spending much of my free time with my friends.
Despite its population of 2 million Bucharest seems quite compact - you can get around quite easily on foot, and the public transport system seems pretty good (I have used the Metro which is excellent). Taxis are plentiful and cheap, but according to my friends you have to be careful because drivers will often try to pull a fast one on foreign visitors (I had one try it on me - he tried to short-change me, but gave me the correct change, with a sheepish grin, when I made it clear that I wasn't having any of it!).
English is not as widely spoken as in many other parts of Europe, but I didn't find this to be a major problem.
One thing to be aware of is the currency - they have just had a currency reform where they chopped off several zeros, but the old notes are still in circulation so you can end up handing over 100 Lei and getting 10000 Lei change.
I don't think you will need a car to get around town, but as you have a whole week you may wish to head out into the country for a while. My friends often spend the week-ends somewhere up in the mountains, I could ask them where.