The bill amounts to around £12,000 and covers the period last year when Ms Truss was running to be the leader of the Conservative Party.
While she has said that she will pay for all personal expenses incurred, she is disputing the majority of the invoice, which she says relates to using Chevening for government business.
She claims that she should not be liable for most of the bill, as it would have been inappropriate for her to pay for officials who were present during the transition preparations, as it would have breached the Civil Service Code.
Ms Truss is still an MP and has been giving speeches about her economic philosophy since she left office. She has ruled out running as prime minister again but is planning to stand again as the MP for South West Norfolk at the next general election.