I thought it was with the Bend Will shout, but I just got killed by a serpentine dragon after I used that stupid shout eight times on it with no effect. My character is level 55 and I play on expert difficulty (not sure if that has any bearing or not). It's really getting kind of frustrating, this is the second time this has happened.

Any advice would be greatly appreciated.

Do you know all 3 words? You need all 3 to tame dragons.

are you using the 3 level shout?
words 1 and 2 of the shout dont work on any level of dragon

Yes, I've finished the MQ in Dragonborn, learned all three words of the shout and used it to tame a dragon in it. I'm pretty sure I used the Bend Will shout to do it. Now, it seemingly has no effect on any of the dragons I've encountered since.

If you are targeting right, i don't know. You point, shout, there is a glow and the dragon comes down

You have to 'hit' the dragon with it, as in like the dragonrend shout.

this is the only other thing i can think of
the shout isnt like an area effect, you have to hit the dragon
and its kinda hard to aim since the effect takes up the whole screen and obscures what you see

It travels in speed and shape similar to Dragonrend, if that helps. Just physically hit the dragon with it and it should be tamed.

Although you used it on a generic dragon, keep in mind that there are some it does not work on.

It works on all generic dragons ( dragon, frost dragon, blood, Elder, Ancient, Revered, Legendary and serpentine) as well as Odaahving. It does not apparently work on any other named dragon that I know of.

You need to know all 3 words of power for the shout to work on a dragon.