I use my flat whisk for this and it makes things super easy!
(My flat whisk could quite possibly be my favorite kitchen tool in the whole wide world. I use it to whisk eggs together in this recipe, or for scrambled eggs, or even if I have a powdered mixture that needs mixed. It mixes it so well! You can see this must-have kitchen tool, along with every other “Must-Have,” kitchen tool in my post: My Favorite Kitchen Tools )
Next, simply pour the egg mixture over the bread pieces and make sure each piece has been covered or submerged to let that bread soak up that amazing custard mixture!

Oh my… doesn’t that photo of the egg mixture just make you drool!? It does me, every stinking time I look at it.
HOW LONG TO BAKE BREAD PUDDING
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I could feast on this dish endlessly