Short answer: most urban trash bins do not come with liners, and you normally buy them separately. Public street bins are usually designed to be emptied directly or to use a heavy-duty reusable internal liner, not a thin kitchen bag. Residential bins issued by the city typically don't include bags either—you're responsible for buying the right size, and your building or city may have rules about what you can use.
If your bin has a removable inner bucket, that's not a disposable liner; it's just an insert that makes emptying and cleaning easier. You can still put a bag inside it if you want, but check local guidance first. Some apartment buildings or private waste services do supply liners, so it's worth asking your property manager or checking your city's sanitation page.
My practical advice: look at the bin's manual or label, confirm whether bags are required, and buy liners separately unless your building supplies them. For public bins, don't add your own liner—just use the bin as intended.