If you've been bitten by your 'tiel over the course of 4 years and just this once came down with a cold/flu, chances are it didn't come from him.
You do stand a chance of contracting some diseases or infections from your bird - though the possibilities are relatively small. If your bird has not been exposed to other, unknown birds or possibly wild birds/poultry and has been healthy in your care (preferably seen by a vet for well bird visits), the chances of passing a disease on to you is even smaller.
Psittacosis/Chlamydiosis is one of the more serious, along with Campylobacteriosis, Salmonellosis, New Castles Disease, Tuberculosis (Myobacteriosis), Giardia, Cryptosporidiosis and of course some others.
These diseases are usually transmitted through inhalation or ingestion of infected feces/droppings or airborne droplets produced by a sneezing, infected bird.
When it comes to catching a common cold from your bird (or giving it to them), it will not happen. This particular virus is generally species specific. You will also not catch your bird's more typical respiratory, crop or intestinal infection.
It would be a very good idea to have your buddy checked at his vet and get a good health profile, including DNA panel done to rule out his carrying any serious disease that might be passed on.
To learn more about dealing with a biting bird, check here
http://www3.upatsix.com/liz/articles/biting.html
Certified Avian Specialist
Cert. Avian Specialist; Int. Assoc.Animal Behavior Consult; Pet Ind. Joint Advisory Council; author