Assuming your budgie has out-of-cage free-flight time, start with a perch next to an open travel-cage door and a small sprig of millet attached to it. Over several days, gradually re-position the millet bribe until the bribe is inside the cage.
Hopefully your budgie will simply follow the bribe as it appears in each new position and when it is comfortable inside the cage, shut the door when you need to be ready to travel.
Plenty can go wrong with this approach but if you are slow & steady in your movements, it can go well.
If you need to do a cage-to-cage transfer, a modified approach is needed!