Will a bladder infection go away on its own?

May or may not . An acute urinary tract infection that is untreated or not resolving can potentially lead to serious problems including an infection to the kidneys. So get it checked out before symptoms get out of control.
It's possible. If your symptoms are mild ( burning, discomfort) you can wait a little bit to see if it clears up. More serious symtpoms like fevers, nausea vomiting, back pain, worsening burning will require prompt attention and treatment.
Some. Increasing your liquid intake, acidifying your urine with cranberry juice and emptying your bladder often all help but if it does not resolve you need to see your doctor.