WELL, I’LL BE WAITING UNTIL I’M OLD ENOUGH: Why You Shouldn’t Wait To Sign Up For Medicare Part B. “He should have signed up for Medicare Part B three years earlier when he turned 65. By delaying, he had missed the best window — the so-called Initial Enrollment Period — to apply for Part B, which covers much of what we consider health care: doctor visits, tests, injectable drugs (including chemotherapy), ambulances, physical therapy and other non-hospital services. As a result, he has to pay permanently higher premiums, and he had to endure an unsettlingly long period — from December to July — before the coverage actually kicked in.”