I actually recommend a jump -> bomb throw -> quickdraw (from a distance) along with simple bomb throwing.
To be more specific:
1. Check the distance. For safety's sake, we want the bomb to land on his feet.
2. Shield (the bubble shield) an arrow.
3. Quickly jump into the air before the next arrow hits (practice the timing on this one). Depending on how far away you are, you may try a double jump to get the bomb to fly further.
4. Throw the bomb at some point during your jump or during the fall (once again, this differs depending on the situation).
5. Land with a quickdraw (arrow cancel).
Now, there are plenty of things that could happen...
A. He'll be hit by the bomb and then stunned by the arrow. Extra damage for you and a brief pause in his spam to allow you to move a bit closer.
B. He'll maybe manage to roll out of the way of the bomb only to be hit by the arrow.
C. He'll shield, allowing you a chance to move forward.
D. He'll try to reflect the bomb using the mirror shield and it will bounce off only to blow up at his feet, ensuring that he takes damage from both the bomb explosion and the arrow.
There are plenty more, and you can rest assured that even if he manages to avoid damage entirely, he's forced to stop his spam, thus allowing you to move forward. Alternate between this and simple bomb throwing, so he's not sure if that arrow is coming or if you're just going to pull another bomb. If you do it really well, he might get frustrated enough that he'll abandon the excessive spam (I'm sure he'll still be doing it every so often just to pressure you) and try a new tactic.
Also, don't underestimate the value of jumping up and throwing an angled boomerang throw in there. If it gets hit by the arrows, it will be negated, but there's also a chance that it might slip in between and hit him. In addition, you can also try using the whirlwind effect to drag him towards you for a surprise attack (so long as you're paying attention). Even if he dodges or shields the whirlwind, he STILL has to stop the spam to do so. Just be careful, because if he reacts before you do, this plan could end up backfiring if the whirlwind pulls him towards you and you're not ready to smash him once he gets within range of your sword.