Yes, as a general rule viruses do not pass between avians and humans so he should be safe. Still being sick is nasty stuff so try to keep him away from all yucky parts of being sick like used tissue paper, or out of you face and keep you hands and stuff cleaner than normal.
I have not heard of any bird getting COVID but If it were me I would be on the side of caution. No close contact with Bokeh - no cuddles or scritches - even if it is not COVID, you do not want to be coughing or sneezing on him. Our saliva is toxic to birds. You may want to wear a mask and wash your hands if you have to change Bokeh's food and water bowls. Maybe it would be better to have someone else do it, if possible. But this is just me - I tend to be on the cautious side. Hope you feel better and it is not COVID!