Appearing alongside, Lloyds chief executive Antonio Horta-Osorio before the Parliamentary Commission on Banking Standards, Bischoff said that as a taxpayer-owned company it should "be very much aware" of the public sentiment towards banking bonuses.
Lloyds is planning an overhaul of the chief executive's bonus scheme, which would mean Horta-Osorio could not draw his 2012 bonus until its shares hit a level where the state was back in profit on its bail-out investment.
Bischoff also backed the chancellor George Osborne's call for the break-up of banks that did not implement the ring-fence plan properly.
The ring-fence will require banks to put their high street banking activities - such as taking deposits and lending to UK businesses - into a separate subsidiary from their riskier investment banking operations.
Yesterday, Barclay's chief executive, Antony Jenkins announced his decision to give up his 2012 bonus, believed to be around £1 million.
He said it would be wrong to accept the bonus in view of the "difficult" year Barclays had just experienced.
"I am aware of considerable speculation about, and public interest in, the question of whether I will be awarded a bonus in respect of my performance in 2012," said Jenkins.
"To avoid further unnecessary public debate on this matter, I wish to make clear that I concluded early this week that that I do not wish to be considered for a bonus award for 2012 and I have communicated that decision to the board."
