If you're asking about State and local taxes, it depends on your state and local laws. Here in Austin, Texas, we have to file separate payments with both entities once per quarter.
If you're asking about Federal income taxes, the answer is "it depends". If you are already required to file quarterly estimated payments (because, for example, you have a regular job with predictable income but also make some large amount of money on the side from a source that doesn't automatically withhold for you), then you might already be making quarterly payments. If so, you should lump in the AirBnB money when you do that. It really depends on how much withholding (if any) you make from your "regular" income. If your AirBnB listing(s) are really successful or really high-priced, then you probably should make add'l quarterly payments to avoid interest and penalties later. Think of it this way -- even with just your regular paycheck, if you under-withhold too much, you'll be penalized (monetarily, not with criminal charges) at tax time.
If you can't do the calculations to know whether you'll be under/over the line, a tax accountant can figure it out for you if you give them an estimate of how much "profit" your listing will generate per quarter.
