Getting on? Getting onto?

Lee asks:
When we board a bus do we say "get on", "get onto" or "get into" it. I was told that it should either be "get onto" or "get into" and not "get on". However I beg to differ. Am I right?

I love the questions that make me think about what I never think about! In this case, I'd say, "Let's get on the bus, Lee." Once we were aboard, I might tell Lee, "Get into your seat before we start."

If someone told me, "Get onto the bus, Crawford," I'd look for a ladder that would let me climb to the roof. But if the bus were that crowded, I'd prefer to wait for the next one.