Embattled Speaker Bronwyn Bishop is seemingly facing more opposition from within her own party, with several frontbenchers reportedly calling for her resignation.

Several senior Liberal MPs have told Prime Minister Tony Abbott he must remove Mrs Bishop from her post if she fails to stand down, The Daily Telegraph reports.

The report also claims the Speaker has charged more than $260,000 over the past five years on luxury car trips to her expense account.

Mrs Bishop reportedly spent more than $1000 on two chauffeured car journeys in Sydney on the same day she attended the opening night of play "Yes, Prime Minister" in April 2012.

The allegations follow a tumultuous few weeks for the Speaker, who was forced to apologise and repay more than $5000 of taxpayer money she spent on a helicopter flight from Melbourne to Geelong.

The newspaper yesterday claimed Mrs Bishop had also charged $6000 to her expense account for a 160km luxury corporate jet flight to Nowra from Sydney for a Liberal fundraiser.