I've worked at an Avian/Reptile Rescue for about 8 years now, and Sailboat made some really good points that immediately popped-into my head as soon as I read your post. Something doesn't sound right here at all to me either...
First of all, volunteering at the Rescue is a great idea if you have the time and want to do it, most Rescues don't have nearly enough man-power, especially an Avian Rescue. Usually though, any new volunteers to a Rescue, at least in my experience, have to go through a "training period", which usually lasts anywhere from a few weeks to 3 months, before they allowed to work with the birds alone without a senior volunteer being with them. Have they said anything to you about training?
I also wear the same clothing to the Rescue every time I go, I don't even bother with washing them when I get home usually, as I'd be washing clothing constantly (I'm there almost every day, and it's usually either in the mid-afternoon or later at night). So I keep the pair of jeans, tee shirt, and hoodie along with the pair of sneakers I wear there in the bathroom that is in the walk-out floor of my house, where the birds are never at. And I wash them typically every other day, depending on what I've been doing or if they get dirty. And the rescue that I work at actually has disposable, paper shoe-covers that go over our shoes each time we enter into either of the bird rooms or the reptile rooms, and are changed every time we go outside for something, or when we walk from one room to the other.
Keep a small container of hand-sanitizer with you at all times in your pocket. I use it after each bird or reptile I handle, especially if there's an emergency and I can't wash my hands right away (I'm the medical liason).
Now, as far as this bird-sitting thing, something doesn't sound right to me either. First of all, if the rescue offers a Boarding/Bird-Sitting service, which apparently they do, then why are they wanting an employee to keep a bird being boarded in their private home? I guarantee you that the rescue is being paid by the bird-owner, and part of the Boarding service is the food for the bird. So there's no way that you should be paying for anything that this bird needs. However, I just don't understand why the rescue would ask any employee to keep a bird that is being boarded with them at their own, private home, let alone a brand-new volunteer that hasn't even started yet.
Here's my issue with this, and I'm coming from the angle of YOUR PROTECTION. Any Rescue, Shelter, Vet Office, Pet Shop, etc. that offers a Boarding-service has not only the permits that are needed to be a Boarding service, but they also have insurance to cover anything that might happen to the animal while in their care...But neither the Rescue's permits nor their insurance are going to cover that bird if it is being Boarded in your home. So you need to realize that anything that might happen to that bird while it's in your home is going to be your responsibility, both legally and financially. So if the bird gets sick and dies, that's on you. If the bird accidentally flies out of it's cage and gets out the door, that's on you. If it flies into a window or a wall, that's on you. And it would most-likely be up to you to sue the Rescue to recoup any financial losses you might be responsible for. So just from this point of view, I wouldn't even consider doing this...It's one thing if you personally know someone and they ask you to take care of their bird for them, and they're paying you to do it, and they know that their bird is going to be in your home and be solely your responsibility. But this bird's owner thinks that they are boarding their bird with a reputable, licensed, insured Avian Rescue...and that really isn't the case at all. And this is going to be for months? No way...
And then there's the risk to your bird. That's a whole other problem, as even if they take their bird to a CAV and get a certificate of health from them, that means absolutely nothing at all as far as whether or not their bird has any bacterial or fungal infections...When a CAV does a "wellness-exam" in order for a bird to be boarded somewhere, they aren't running fecal cultures or crop cultures to check for bacterial or fungal infections. And you know how well birds hide any outward signs of illness, pain, etc. So this bird could be sick right now, get a CAV to do a wellness-exam and get a certificate of health to be boarded, and even if you do the 30-day quarantine in a separate room from your bird, the likelihood of your bird contracting any infections, diseases, etc. that their bird has while being inside your house is very present....No way, not a good idea at all...Then there is the factor of attention and care for their bird. I mean, this Sun Conure isn't going to be happy being locked inside a cage with no attention from anyone 24/7 for "months". It's going to scream and scream and be miserable, and rightfully so. So that means you're going to also be responsible for giving this bird the amount of attention and stimulation it needs to stay healthy and at least happy enough that it doesn't start screaming and god forbid plucking itself, because that will be on you too...
i'd absolutely say no to doing this. There's nothing at all wrong with boarding your bird at an Avian Rescue, but the bird needs to be boarded at the Avian Rescue, be the rescue's responsibility, and liability, since they are the one's with the license and the insurance, and they don't have a personal pet bird that could drastically be effected by the presence of that bird being in your house...And you certainly don't want to be responsible for anything that happens to that bird. There's just no reason for them to want to send a bird that they're being paid to board by a private individual to the home of a new volunteer, so it can be their problem and responsibility...This is just a bad idea all the way around for you and your bird...It's great for the Rescue, lol, they're getting paid to do nothing and take no responsibility for anything, nor will any of their pets be potentially in-danger...