You're cutting it very close with Bran on the 31st and then Rome on the 1st of November...I don't know where you have your flight from, but it'll probably be a really sustained sprint for you.
If you land in Bucharest - most likely -, you'll be about 4 hours away from Bran Castle, by car. To be fair, you'll probably have some time to walk around Brasov and then go to Bran. I recommend eating and partying in Brasov, as well as accomodations. Since you're there and if you'd like something a bit more spectacular to see by comparison to Bran, you could take a train / car to Sinaia and see Peles Castle, or to Sighisoara, all of which should be manageable in a day.








