What does Banquo mean when he says 'question this most bloody piece of work to know it further' and what does that reveal about his character?

Banquo is already suspicious of the effects he fears the prophecies of the Weird Sisters have had on Macbeth. Remember, he was there when they told Macbeth that he would be king. When Duncan is killed under Macbeth's roof, the accused "murderers" have been killed so they cannot defend themselves, and Lady Macbeth conveniently faints so that more questions are deflected, Banquo's suspicions begin to be confirmed: Macbeth is behind the king's assassination.
Banquo is Macbeth's foil in the play; he is actually the man of character and ethos Macbeth pretends to be (and may actually have been before the temptation of the witches and his wife's persuading bring his lesser nature forward). This exchange is key:

MACBETH
If you shall cleave to my consent, when 'tis,
It shall make honour for you.
BANQUO
So I lose none
In seeking to augment it, but still keep
My bosom franchised and allegiance clear,
I shall be counsell'd.

Macbeth seeks to ascertain if Banquo will side with him when all is revealed. Banquo, however, makes it clear he will not go along with anything that stains his honor. At that point, Macbeth realizes he will have to get rid of Banquo as well.