それとも is simply a conjunction. Also, remember that Japanese is a high context language, so you don't necessarily have to include everything in a sentence if it can be understood from context. Simply asking 一人でパーティに来ましたか or 友達と来ましたか should be acceptable since if the answer is no, then it implies the opposite case.
And to nitpick a bit, it's どうもありがとう, don't forget the long vowels.