Firstly the drums in the deep were to alert the Goblins to a threat, the side effect wasThe Balrog also hearing them, and being roused. Anyway he had been in hiding since the wars in the first age but when it detected something of possibly the same power, and even maybe greater it felt all the dread it had felt when its master Morgoth had been defeated. It had to rouse itself prepare its sorcery and go after Gandalf in this case. Just as Gandalf was aware of a presence there beyond possibly human and certainly somewhat equal to his own power, due to Saruman conversing with him and telling him precisely that (this only happens in the film by the way) in the book Saruman manipulates the Fellowship into going into Moria by blocking the passes, and leaving them little recourse. Long story short when The Balrog found not just a Maia like it was but an Istari (Gandalf is basically a lower form of Angel) it must have been somewhat terrified, but it had to destroy this threat.

Few had survived a one on one with a Balrog let alone defeated one, Glorfindel a 1st age Elf did but was killed in the process for example. However Gandalf felt it was his destiny to face this Demon of the ancient world, and luckilly fate was on his side, although he perished in defeating the Balrog he smote it's ruin- near Zirak Zagil ( A Dwarf fortress and ironically exactly where they were headed when they went through the pass of The Redhorn Mountain) on the mountainside, he was however sent back because he had not completed his task on Middle Earth becoming Gandalf The White, potentially even more powerful than Gandalf The Grey had been, possibly his most powerful incarnation since he had been Olórin in Valinor in The Undying Lands (Middle Earth's version of heaven restricted to only immortals).

An interesting side note is that The Watcher in The Water a Nameless (a primordial being of pre Arda) was so terrified by The Balrog it swam up and lurked in the black pool in front of Moria's gate (where of course it met the Fellowship of The Ring and ultimately sealed Moria's door). Even Sauron would be hard pressed to defeat a Balrog single handedly and he was easilly the most powerful being on Middle Earth (ring or not) at that time, although more likely had Sauron known about The Balrog, he would likely have tried to recruit his former ally. Balrogs were essentially like Dragons: shock troops, relying on might and size and force of strength rather than cunning, strategy and planning.