Being a new birdie owner myself, after the initial "ooooh, what's THAT mom?" from my two cats, they usually just hang out on the bed while I'm in the living room with the bird. Or sleeping on the sofa, occasionally opening one eye to see what the bird is currently doing (she sticks very close to me, her favorite place when out is on my shoulder - I try to encourage her to explore, but she just climbs right back up so she can preen my hair and ears).

I am very aware of where the cats are at all times, and Diamond the dog is 10 and more interested in sleeping and has shown no interest in the bird at all.