I don't know how it works in the US, but when you buy in the UK, what's important is that you demonstrate your ability to pay.
That means through your regular income - savings, employment, investments etc you demonstrate you have the money to afford repayments.
I don't think you can include BNB income as it's not guaranteed.
Best to speak to a mortgage broker.
The important thing is to do your sums, so you are confident you can afford repayments whether or not you are able to let it out through Airbnb (and of course that where you are buying allows Airbnb).