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Bound to bust, I'm sure (2,5)

Ross

I believe the answer is:

no doubt

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'i'm sure' is the definition.
I can't tell whether this definition defines the answer.

'bound to bust' is the wordplay.
'bust' is an anagram indicator.
'bound'+'to'='boundto'
'boundto' anagrammed gives 'NO DOUBT'.

Can you help me to learn more?

(Other definitions for no doubt that I've seen before include "Surely" , "To be sure" , "sign of agreement" , "Almost certainly" , "Bound to, unquestionably" .)

I've seen this clue in The Times.
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