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.
