I don't know if you have checked out pet general yet but there have been some threads about birds there and how they interact with other pets in the house. I have an older cat and a young parakeet who get along fine as long as I don't let the bird fly loose in the same room as the cat. My cat has never been a bird hunter and never tries to jump at the cage so they get along fine and can even sleep in the same room as long as the parakeet is in the cage. The worst thing my cat has done is make big eyes at the bird when he is noisy.
Anyway, I think that if the bird is new it will take some time for them to adjust to each other. Take it slow if either one is uncomfortable, don't force them on each other. Keep them in separate rooms if you have to. A lot of people here say they are afraid that their other pets will hurt their bird so it seems funny that you have the opposite problem.Good luck!