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!)