OK! This sounds like mites to me rather than fleas.
The red mite (which will appear black before it sucks blood), only lives in the cage/aviary and sucks the birds blood at night, which is when it comes out.
The best way to treat this is with careful use of a delousing powder such as a parrot permithrin dusting powder or 'Harkers louse powder'. Your local pet store should have a mite/louse powder which will kill these night time blood suckers.
Also be sure to clean all perches/corners for any that are living there.
Yes, i'm afraid you will have to catch him! That's best done using a towel to hold him- and then hold the back of his head between your first finger and thumb to stop him biting you! Then get another person to dust some powder under his wings and on his belly area- if you can then quickly turn him over and dust a small amount on his back- try to get the powder to the base of the feathers for best effect.