The letter, organised by Greg Hands, said Mrs May could not bind her successor to a deal so any agreement with Labour was likely to be "at best temporary, at worst illusory".
But Mr Bone said unless there were substantial changes to the Irish backstop within the Withdrawal Agreement, it would not be backed by MPs. It would be followed by negotiations on a new trade deal with the EU.
He said: "We have been at this five weeks, we haven't seen the significant shift yet that we require to be able to support a deal".
He said the Tories "may well have to concede that there is a public vote of some sort" on the deal.
Ministers are split on whether asking parliament to choose its preferred Brexit, probably based on ranking different options, is a Trojan Horse to deliver what some see as an appalling Brexit in Name Only, a disgraceful abdication of responsibility by government, an impractical and total waste of time or a longshot that is worth exploring given that all other initiatives to secure a departure from the European Union have failed.
The Prime Minister is understood to have requested the meeting, and also dispatched her chief Brexit negotiator Olly Robbins to Brussels for two days of talks about the possibility of making changes to the Political Declaration to strengthen protections for workers rights and request a say in future European Union trade deals for the UK.
Madonna rejects calls for Tel Aviv Eurovision boycott
The group's website says "Israel effectively declared itself an apartheid state by adopting the 'Jewish Nation-State Law'". A group of celebrities - among them Stephen Fry and Sharon Obsourne - signed a counter open letter rejecting the boycott.
Kang claims AT&T Byron Nelson for first PGA Tour win
The weather did little to dampen Nicholas Lindheim's day, however, with the American within a chance of shooting his own 61. Twice over the last two days, Every overcame deficits of at least four strokes and went ahead of Kang.