The most common and most likely answer to this crossword clue is the 8 letter word GROSBEAK
I've seen this crossword clue in The Times
G
R
O
S
B
E
A
K
Buddy explains!
The straight part
We know that "one’s got a hefty bill" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one’s got a hefty bill = grosbeak.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 GROSBEAK mean?
GROSBEAK noun- Any of several finches and cardinals that have a large, powerful bill