Bread isn't toxic, but it offers parrots almost no nutrition and most loaves carry meaningful salt. Tiny pieces of whole-grain, low-salt bread only.
What it means for budgies
There's nothing specific to a budgie that changes the verdict on bread — it's treated the same as for parrots generally. A budgie portion is tiny — a single bite or a little grated amount is plenty.
The full picture on bread
Bread is empty calories for a bird — refined starch that fills the crop without delivering vitamins or minerals, plus added salt in nearly every commercial loaf. A bird filling up on bread is a bird skipping vegetables and pellets.
Whole-grain, lowest-salt option, in tiny amounts.
Never as a meal replacement or daily ritual.
Skip anything with raisins (sugar), garlic, onion, or seeds coated in salt.