What is it with people and cohabitating animals? I get a lot of Google hits on queries like "can I keep my bearded dragon with *insert animal of choice*". I've written about bearded dragons and land hermit crabs before here - amazingly bad idea to put it mildly. Desert animal and animal needing high humidity. Why would you want to keep them in one cage?
Then came bearded dragons and gerbils. Yeah, the dragon will appreciate the snack. And he may suffocate on it as well, killing both your pets in one go. Congratulations.
And now it's bearded dragon and budgies. See dragon and gerbil for result. If you think that the dragon can't catch a budgie, you have never seen a fully warmed-up dragon run and climb. In the wild, he wouldn't stand a chance, but in an enclosed space, the bird is dinner.
Please don't even think about trying this, even if the species may seem to fit well with each other or live in the same habitat in the wild. That's in the wild, not in a tiny cage (compared to their natural habitat). Cohabitating species is not a good method of saving space and being able to keep a ton of animals all at once. There are a few species that may be able to cohabitate in a huge enclosure, but that requires a lot of experience of keeping each species on its own before you try it. You must also be able to separate the species at the first sign of trouble and not in the "oh shit, it doesn't work out so the crab/gerbils/iguana has to live in a Rubbermaid tub until I can get the money for a suitable enclosure"-sense.
Bearded dragons are not really suitable for cohabitating due to their inclination to try and eat anything even a bit smaller than themselves, which includes other dragons.
If you don't have the room and/or money for a second enclosure, you don't have the room and money to care properly for the animal at all, period.