i'm sorry to hear about the bird.
now, as to B's and small animals, i have to fairly say it is up to you, the B,and the small animal in question. i got my boy socialized EARLY with all sorts of small critters. He grew up with rabbits, guinea pigs, birds of all sorts, cats, dogs, and such.
Zumi has never harmed one of my tame rabbits, but has tried to eat some wild ones. He never harmed any of my tame birds, but has tried to eat outside ones, same with cats. Some B's can do fine, ALWAYS supervised of course, and some are hell with small animals. It also depends on the small animal. has it ever been around a dog? how will it react to being sniffed/licked? will your bird flap and screech? will your bunny run? here are some pictures of Zumi with some of my small animals.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/IMG_0787.jpg
Zumi inspecting the Quail cage. he never got to them, and they were kept in a high/B-safe place at all times.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/2Img_0632.jpg
Zumi sniffing a baby bunny. he only ever sniffed them. but they held still, i am sure if one bolted he would have chased. He was raised with rabbits, i generally ran a rabbitry of over 100 rabbits.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/Img_0586.jpg
sleeping with the cat. he ADORES cats. would chase then pounce and lick them.. never hurt them.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/Img_0567.jpg
Zumi with a pet rat. he could have cared less for them.
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/Img_0243.jpg
http://i93.photobucket.com/albums/l75/BlauesHaschen/dog%20show%20pics/Zumi/Img_0244.jpg
Zumi's first meet and greet with a very dog-friendly rabbit. Ben was used to dogs, and was calm, not all small animals are. that's the biggest thing to keep in mind. How will the small animal in question react? and can you keep it safe if your B decides its not friend, but food?
it can go either way. its good to have advise from all sides and experiences.