Tips on how to memorize the formal names for bones and other parts of the body?

Part of being able to consistently do this as you learn more anatomy or even biology is to understand the root words.  Such as "foramen" is a whole, "cleido-" means clavicle, "osteo-" refers to bone, and so on.  If you understand why that part of the anatomy is named that way, it's easier to remember them than trying to come up with some grand mnemonic that covers everything.

This is true is of all biology.  Memorize the basics, but understand the rest.

if you just have to know the names of the bones and not features on them my advice is to just keep repeating them from head to toe in your head, and listing them on paper from memory while picturing the skeleton. If you go section by section you will be surprised how easy it is.
Start with the skull and move down -
pectoral girdle (scapula, clavicle),
arms and hands,
vertebrae (cervical, thoracic, lumbar),
ribs,
pelvic girdle (pelvis = ilium, ischium and pubis, and the sacrum),
legs and feet

The one that is easiest is the ulna. The head of it is shaped like a U and is what people commonly call the funny bone because thats what you hit when you hit your elbow.