Just making sure, but you do have the dex requirement for the bow, right? If not, there's your problem. Otherwise, yes, he's bugged so go back to the bonfire. Took me 150-180 shots with wooden arrows for reference.
i've pumped like 100 arrows into him with a longbow +5, dex build with 25 dex. i destroy the tail then start shooting at his head. after about a quarter or less, he just does this head shake thing and heals? idk, im thinking he's invincible until i do something. but i rang both bells already :(
gladly awaiting TESV:Skyrim, Resistance 3, Dark Souls, and Mass Effect 3
Anyone "killing" the Drake with arrows should post a youtube video. It's not a glitch, the Drake heals himself around 1/2 HP. Watch his health, and around 1/2 HP he puts his up to his wing, and regens to 2/3 HP. Arrows aren't strong enough to finish him off, you need to either melee him on the bridge at that point, or make him fly a lot to make him suicide (he land in the wrong spot, and accidentally kills himself).