Try and identify the type of bugs you have. There's probably a website for infestations and stuff which might help identify them.
Depending on what you have and how bad it is, you may have to get your home fumigated. If you can't find the source, you'll probably best to call in an expert, especially if you keep finding them.
If you can arrange for your bird and other pets to go elsewhere with family of friends while the issues gets sorted it would probably be best for them.