Hi there,
I happen to have a lot of rabbit experience as I raise and show French Angoras, I board my personal animals at this time with my best friend and rabbitry partner but I've been a serious hobbyist for about 10 years.
Rabbits are prey animals and as long as you learn their body language and know what to look for as far as stress or agression you'll be fine. The first response of a frightened or ticked off bunny is a loud thumping of their back feet against the floor, often they will do so multiple times in rapid sucession. The ears may alternate between being forward towards the percieved threat and laying flat back against the head and body (assuming your rabbit is normal earred and not a lop). Just foot thumping is typically a fear reaction.
Aggression or self defense will present itself with the rabbit being leaned forward seemingly on its toes, body tense and ready to leap toward the threat, head held low and neck extended, ears back. The bunny may vocalize by grunting or growling.
A scared bun will typically hop away from the threat into a nearby corner, back into the wall, facing out, ear forward listening, and then the thump comes. It can be quite loud on a hard floor.
My rabbitry partner has kept her many rabbits in very close proximity to her own birds, a conure and a cockatiel for a couple of years and has never had any issues with bird or bunny illnesses though the rabbits do not directly interact with the rabbits.
Pasturella AKA Snuffles is a disease that many Vets believe the vast majority of the worlds population of rabbits have been exposed to. It can lie dormant in the system of a rabbit for either its entire life never showing itself or it can present symptomatically after a stressor to the rabbit. There is no vaccine for Pasturella, nor is there a cure. Typical treatment is a antibiotic which can qwell the symptoms for a time but it will never go away. Pasturella is airbourne and can be carried on clothing and shoes. The most common symptoms are sneezing, white nasal discharge, and crusty front paws on the inside from the rabbit wiping its nose. The rabbit will be lethargic, go off feed, and may be listless. Breathing will be noisy and the chest may rattle.
All of this said I've know several bunny breeders who also either had pet birds or who were also bird breeders and I've never heard of a bird contracting Pasturella from a rabbit. I will find you some links on this in the morning but if it were a major concern just handling a rabbit could track it into your home on your clothes or shoes so actual interaction between bird and rabbit would not be nessesary. My thoughts are that there are most likely two different strains involved, a bird strain and a rabbit strain. I'll look into it since I have a lot of rabbit medical literature.
Sincerely,
Jenna