"I can not see how an agreement that has been rejected three times by Parliament would not be rejected a fourth time", Mr Bone told talkRADIO's Julia Hartley-Brewer.
That would leave just two options when the October 31 deadline looms, a no-deal Brexit, which has previously been rejected by MPs, or the revocation of Article 50, cancelling the entire process.
Parliament has three times rejected the divorce deal May and the European Union struck late previous year.
Despite the hope for clawing back support by making it explicit that the Conservative party supports the democratic will of the British people - something apparently unclear under the leadership of Theresa May - Blunt seemed to also accept that much of the damage was already done. "It is the same thing again, again and again".
At one point, the Prime Minister will be replaced.
Cross-party Brexit talks between Labour and the Tories have so far failed to produce a compromise agreement.
Asked if she would resign if the bill was defeated, May told reporters she was sure Members of Parliament (MPs) would keep in mind to respect the referendum result.
"We don't think there is a deal there yet", Labour economy spokesperson John McDonnell said.
Lawmakers from the upper house of parliament had earlier asked Barclay if this was "the last chance saloon" for May's divorce deal.
May's chief Brexit negotiator, Olly Robbins, is due in Brussels to discuss changes to the political declaration on the UK's future relationship with the EU.
"It is imperative we do so then if the United Kingdom is to leave the European Union before the summer Parliamentary recess". "MPs have already rejected her European Union withdrawal agreement 3 times".
An anti-Brexit protester is pictured outside the Houses of Parliament in London, Britain May 15, 2019.
No 10 would not put a timeframe on publishing the bill, which MPs would expect to happen before the Whitsun recess at the end of next week, but it insisted the vote would happen that week.
Before her deal was defeated the last time, 344-286 on March 29, Ms. Keir Starmer and Tom Watson have estimated that up to 150 Labour MPs would refuse to vote for a Brexit deal that did not have another referendum attached. It would be followed by negotiations on a new trade deal with the EU.
But Mr Bone said unless there were substantial changes to the Irish backstop within the Withdrawal Agreement, it would not be backed by MPs.
Speaking at the launch of her own campaign at a whisky distillery near Stirling, she begged Tory voters not to back Nigel Farage on May 23 - and suggested that those MPs not spreading the same message are admitting failure.
The Prime Minister is set to force a vote on her Brexit blueprint in the first week of June - regardless of whether she has agreed a compromise plan with Labour in cross-party talks.
May faces a punishing week when the Commons returns from recess, including the vote on the withdrawal bill, a three-day visit from Donald Trump and the Peterborough byelection, a tightly contested seat being fought by the Tories, Labour and the Brexit party.
Some 13 former ministers, together with the chairman of the backbench 1922 Committee, Sir Graham Brady, have written to the Prime Minister urging her not to concede Labour's key demand.
"What she (May) is working to do is to get a deal passed as soon as possible", the spokesman said.