Just dreaming of a bird flying into the house is a good sign in itself.
However, if you dream of birds flying around, or you shoot birds yourself, trapping birds means that you will encounter misfortune or break your money.
So, it depends on what the bird in your dream is doing. If you just fly into a bird and it doesn't do anything else, it means that you will have good luck in the near future. If the bird finally flies away, it is a good sign.
If birds are fighting, trapped, and flying around, be careful that they may lose money or even encounter disasters recently.