I was wondering that, too

Both "Entschuldigen Sie mich" and "Entschuldigung" are correct translations of "Excuse me." The first one is a bit more formal.

You might use "Entschuldige mich" in case you know the addressee very well and can talk colloquially with him. However, it has a slightly strange sound to it, mainly because it is never or seldomly used.

If you pour coffee on someone on the street by mistake (or also intentionally), you will either say: "Entschuldigen Sie mich" or else "Entschuldigung". If you pour coffee on your brother, you will say "Entschuldigung", or (rather unlikely) "Entschuldige mich".

"Bitte entschuldigen Sie mich" and "Bitte entschuldige mich" are both possible.