There's actually loads of idioms used for that phrase...

"**Without a shadow of doubt**" is the most common and only one which includes the word "doubt"

i.e. "Without a shadow of doubt we will win the next game"

Many phrases make use of the word 'blind' meaning the subject has more confidence than they can see, i.e. "**Blind Faith**" or "**Follow x Blindly**" means you have no doubt in whatever x is.


Also there are phrases that use the word 'Sure' like '**Sure as Shootin**' (American specific) or '**It's a sure thing**' meaning nothing can go wrong.

Other phrases include: 

"All but won"
"(We got this) **in the bag**"
"(It's gonna be) **a slam dunk**"


But coming back to your original sentence, A couple of ways to make it work are:

 **"We've been working together for quite some time now and I never saw him make a mistake, henceforth I am taking his bugs blindly."** probably the most accurate usage.

   "We've been working together for quite some time now and I never saw him make a mistake, henceforth I am taking his bugs without a shadow of doubt."

 "We've been working together for quite some time now and I never saw him make a mistake, henceforth I am taking his bugs as law."

 "We've been working together for quite some time now and I never saw him make a mistake, henceforth I am taking his bugs on the chin."

^^ this last one is quite interesting and specific, but it would work in your example if you're trying to say "something might go wrong, but I don't care I'll be ready for it" so more about confidence than lack of doubt. It's a boxing metaphor so his bugs are like an opponent in the ring you're not scared of.