All you need to do is remove the eggs as she lays them, and do not let her incubate anything. Budgies will lay an average clutch of 4-6 eggs, and will NOT continue to lay eggs if you take them away as she lays them. (Budgies can't count).
If budgies can't count, how do they know when they have laid four to six eggs?
I have more experience with egg-laying in chickens rather than budgies, so I was curious to know how this works. Removing eggs from the nest definitely does not stop a chicken from laying. Quite the opposite, in fact.
After doing a bit of research, I learned that bird species can be roughly categorized as either determinant or indeterminate egg-layers. Determinant layers, like doves, pigeons, and some seafaring birds, like gulls and albatross, will lay a fixed number of eggs. The clutch size is unaffected by addition or removal of eggs. In contrast, indeterminate layers will replace lost eggs if the eggs are removed prematurely or lay fewer eggs if additional eggs are added to the nest. Repeatedly removing eggs can cause an indeterminate egg layer to continuously produce eggs, far in excess of the normal clutch sizes for that species. Chickens are indeterminate egg layers, along with many other bird species.
The desired clutch size varies widely between species, from just a single egg to dozens of eggs. It is theorized that the nesting bird's "brood patch" is involved with determining clutch size and halting egg production - the feeling of the eggs against the bird's skin stimulates hormones that trigger egg-laying to stop when the nest is "full". This is why dummy eggs can be a useful tool to reduce egg production in indeterminate layer bird species.
So what about budgies - Are they determinate or indeterminate layers? Well that's where it gets interesting. Similar to gulls, they will lay eggs every other day, and start incubation immediately. The typical clutch is 4 to 6 eggs. Budgies are considered to be determinate egg-layers by many sources. But budgies sometimes exhibit characteristics of indeterminate layers, like excessive egg-laying.
Digging deeper, I found an interesting article that looked more closely at the timing of egg removal. In short, if the budgie was allowed to sit and incubate the first egg, with all subsequent eggs being removed, the laying pattern was fixed and laying would stop after 4 to 6 eggs, but if the first egg was pulled immediately, and all subsequent eggs were also removed quickly, so the bird was never allowed to incubate for longer than eight hours, indeterminate egg-laying was demonstrated. Budgies in the experimental group (early egg removal) laid over twenty eggs and showed no signs of stopping, compared to the other group, which laid the normal amount of eggs for their species.
The results of this study strongly suggest that budgies are in fact, not determinate egg layers, but rather semi-determinate. A true determinate egg layer is not affected by manipulation of the nest, like removal or addition of eggs. The number of eggs is determined entirely by internal factors.
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What does this mean for budgie owners?
If budgies were true determinate egg layers, there would be no point in using dummy eggs. You could simply pull all eggs immediately and the bird would naturally cease laying after a fixed number of eggs. But since they do show some indeterminate tendencies, leaving at least one egg in the nest - boiled or fake - is the better choice. You can safely remove further eggs, but should leave one dummy egg in the nest to help trigger the end of laying.
I wasn't able to find a good egg addition study in budgies, so I don't know if adding eggs would shorten the laying cycle. I would guess it does not.
Also, keep in mind that laying patterns differ between bird species. Cockatiels, for example, are indeterminate layers, so dummy eggs can be very helpful for curbing excessive egg laying. But doves and pigeons are determinate layers. Dummy eggs would likely not be effective for them.