Because you did not also sign up for Part B when you turned 65 and were not working, you are eligible only during January thru March (General Enrollment Period/GEP) to make a request for Part B by contacting Social Security. Social Security will delay your effective date for Part B until July 1 of that year. You may also be required to pay a late enrollment penalty of 10% on top of the current Part B premium for each 12-month period you could have had Part B but did not take it.
Once you have both Part A and Part B, you can elect to go onto a Medicare Advantage/HMO plan or a Medicare Supplement/Medigap policy and stand-along drug plan to be effective 7/1.
If, when you became eligible for Part A, you did not enroll in a drug plan and do not have creditable coverage for your drugs, you will incur a penalty of 1% of the average national premium for every month you were eligible and did not enroll. This amount is added onto your drug plan premium in perpetuity.