Bumpy Car Ride After Rhinoplasty?

The biggest concern is a nosebleed. If you are travelling and develop a nose bleed, you will need medical attention.
In your case, if the ride is bumpy you should try spending the first couple of days in a hotel after the surgery. On the thrid day you should be able to handle the bumpy ride. During the ride make sure you are taking pain medicine to be comfortable and applying soft ice packs (not hard) to minimize the chance of a nose bleed.
To make a soft ice pack, mix water with rubbing alcohol in a ziplock bag and freeze it.
Regards

It is not advisable to place ice on the nose after a rhinoplasty. The nose will be numb after the procedure, with this decrease in sensation you risk burning the area with ice. The bumpy ride itself will not hurt your nose, but it may cause nausea and vomiting. You may consider getting a hotel room close to the office where the procedure is being performed and drive home the next day.