Budgies in specific but all parrots are flight animals meaning if they get startled they will just leave, because of this it can take some time to build the trust of a parrot. I have complied a short list of things to do to ensure you gain your budgies trust. Please remember this does not happen over time and it does take time and patience.
How to Gain Trust
Positive reinforcement only
Hand feed favourite foods
remain calm and avoid big movements
listen to what the bird is telling you through body language
include them in your daily life – when safe to do so