we thought bed bugs too but the bites aren't like bed bugs at all and we've thoroughly cleaned my bed multiple times[/QUOTE
If you react to bug bites, your bites may not represent what you'll find for bed bugs or fleas. Are all the dogs on flea control program?
Mites that would affect your bird typically would not infest a person, they survive on bird blood, so are likely looking at a different type of mite infestation if it is mites or bed bugs.
Thoughts on bed bugs... we cruise a lot and I'm paranoid about this, so have read way too much, but can share a product that can help without replacing everything... I usually take a spray bottle with me on a cruise and pull off the sheets / bedding, spray down the mattress even if I don't see any signs... even spray our empty luggage before sliding under the bed for storage

But again, paranoid behavior!
Cleaning your bed won't get rid of bed bugs... to be sure it's not bed bugs, pick up two mattress type covers that are plastic / vinyl and zip. Find Nix spray for bed bugs and spray down your mattress and box spring (if you use a box spring) all sides, top and bottom, then put the zip cover on it. If there are bed bugs, mites, fleas or any creepy crawlers, this should kill and solve the problems Toss your pillows and buy new. Put all your sheets / comforter thru washer at least twice. Spray down the floor in your bedroom as well and let it dry - presuming your bird is not living in your room. If he is, remove him from the room. The Nix is not directly toxic, but would keep your bird a safe distance just for safety.
If not one else in your home has bites or any issues, I would sit and think of where you go daily - are you around stacks of paper or work somewhere with sand? If it's not in the home, you might be exposed at work or such.
For your bird, if you think there is a chance, I would say straight to the vet, no questions asked, do not try to treat a bird yourself for mites. Birds are so sensitive to chemicals and such, it's not a chance you want to take. But, the vet can do skin swabs and see if there is anything going on.... good time for a full checkup anyway right!?
Good luck!! We have dealt with snake mites and they can be a beast to get rid of, but we've never had bites and both my daughter and I get nasty welt large nasty bites from bugs or spiders.