You first have to understand what is tail bobbing.
Unlike people, birds lack a diaphragm that separates the chest cavity from the stomach. The muscles located at the base of the tail help birds breathe by playing a part in expanding their lungs for air intake.
If a bird is having trouble breathing, the tail muscles work harder, causing the tail to bob up and down.
If it's a slight tail bobbing, it's fine. It's not actually tail bobbing, it helps the budgies to keep balance and stay in the perch.
BUT, when it's a bigger one, like this one:
you have a respiratory illness, contact the vet ASAP