How long for the hot water to stop smelling with anode rod change?

You should have flushed the tank , this should be done once a year with a check on the anode and you may get 2x normal life or that has been my experience in the past. Also purge as much of the air out as you can and make sure the temp is high enough to kill bad stuff. -140 F is my minimum. But you can still flush it without taking the rod out.