I meant to reply to this sooner but didn't have time.
My cat Samantha has been fine with our parakeet T-bird for 3 years now.
Here is a photo of them together.

Samantha has never done anything more than stare at T-bird from a distance like in the photo above.
I just took a peek at your house tour thread and I think that you could get a bird and Blueberry would be fine with it.
Does Blueberry ever climb on your countertops? Does he spend a lot of time in your room?
I think that if you kept a bird in your room or in a room with a door you could close when you are not there to supervise that it could work out.
Good luck!