Senegal Parrot named "Kane"; Yellow-Sided Green Cheek Conure named "Bowie"; Blue Quaker Parrot named "Lita Ford"; Cockatiel named "Duff"; 8 American/English Budgie Hybrids; Ringneck Dove named "Dylan"
I wish I did, but every pet insurance policy I've ever looked into was either way too expensive compared to just paying for the vet out of pocket, or more often the policies didn't cover anything practical or needed at all. Maybe someone else will comment who has found one that is worth paying for, but I doubt it, not in the US anyway. Apparently the pet insurance that you can buy in other countries, such as in Canada and throughout the UK, is very reasonable and covers everything, and is comparable to our human health insurance in the US.
Personally, we just keep a savings fund for emergency vet expenses and leave it at that. $1000-$1500 would be good for a single bird, more for multiples or XL birds like macaws/large cockatoos. You may also want to set aside more if your bird is female, as they can sometimes develop issues from chronic egg laying. Unless your bird has some kind of chronic condition (in which case I'd doubt you could get insurance anyways), I see insurance as a needless monthly expense you'll probably end up forking over more for in the long term than just setting aside money specifically for health care. It's rare for pet birds to get the kinds of illnesses which would necessitate huge vet bills for treatments out of the blue. Most expensive health care is for older rescues who have been fed horrible diets and/or had prolonged infections and/or have been exposed to environmental toxins like cigarette smoke that has caused permanent damage the new owner must treat. 99.9999% of those kinds of problems can be prevented by simply taking care of the bird, being informed, feeding a healthy diet and ensuring the bird stays active.
We are one of those odd people that have over and over again, rescued older Amazons. And, what has been stated above is true. They are expensive!
And as a result, we have looked into Pet Insurance and, once again as stated above!
The best place to start, in this case, is not here or the internet, but at your Vet's Clinic. Set-up an appointment with the Office Manager /Accounting Manager. Get any kind of insurance, even the best, has no value if your medical service provider does not except it, or require that you pay the bill at the time of service and have the insurance provider repay you!
Many Vet Clinics have different payment packages for their Clients. Like programs that set-up advance payments, etc... Also, programs that support 'active' Clients.
Pet insurance for birds can be much more difficult to get than for, say, dogs or cats. Pet insurance for birds may not cover pre-existing health issues or older birds.
Now, if you buy a bird and it grows old on that health insurance, that's one thing... but if you go out and buy an older bird, that could be something else.
Unless pet health insurance has changed any in the past few years......
If you are in the USA, one option is Care Credit. It can be used for human *AND* pet health! If you spend over $200 in vet fees, you qualify for interest-free payments as long as you pay off the balance in the allotted time. This could be in 3 months, 6 months or longer - whatever the promotional due date is.
Now, you do need to have some sort of income and, I think, a decent enough credit score. What the specific requirements are though, I don't know. The first few times I tried applying for it, I was denied but I did eventually get one! (having a better job certainly helped!)