The most common and most likely answer to this crossword clue is the 10 letter word SWEETENERS
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Buddy explains!

The straight part
We know that "suggesting bribery" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case suggesting bribery = sweeteners.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SWEETENERS mean?
SWEETENERS noun- Something added to food to sweeten its taste, especially an artificial substitute for sugar.
- Something given or added to added to a deal to sweeten another's attitude, especially a bribe or kickback.