male budgies are quite happy on their own usually - we got ours a wife and he wouldn't bother with her, so she went out into the aviary, leaving him on his own in his cage. he seemed a lot happier out of her company.
he's quite happy - he plays with the dog. and enjoys kissing that quite handsome budgie in the mirror!
best to ask the neighbours if getting a bird though, they can be quite loud and your walls may not be the thickest.
a dog, when you're out for 12 hours a day... even with a dog walker/pet sitter, it's just not going to be fair really.
you could possibly get away with a cat, if it had access tot he outdoors, but as mentioned above, any rescue centre will likely say no.