[Voralphion]

I think the reason that Gandalf stayed to fight the balrog rather than running away from it was because he knew that it needed to be killed, and he was the only one who could have defeated at that moment. He didn't want the balrog to overcome its shyness and come out of Moria and start attacking things (especially Lothlorien) so he stayed to defeat it. No-one else in the fellowship could have defeated it, and only a few others in middle earth could have done so (Glorfindel maybe others) but the elves were leaving and may not have cared or been bothered to fight a balrog.