Can the driver stay with me if I have a medical appt?
The Guru Take
Completely up to the driver
There are no strict policies set by Uber or the law on whether a drive can come with you. I think it is up to the drivers on suspending their shift and coming inside.
If you want to ask them to wait for you outside, while they keep the meter running, I think some drivers will agree to that. Remember, you will continue to incur expense while he or she waits for you.
While the drivers will be making money, they could be making more money if they found other passengers, as they get paid more while the car is moving. You may want to be mindful of that when you ask.