The legislation was unveiled in May by the SNP's constitution spokesman Mike Russell and is intended to provide a legal framework "for the holding of referendums on any matters within Scotland's control".
It does not specify the date, question or referendum period - which would all be set by secondary legislation - and has yet to be passed by MSPs.
It was revealed today that Labour's James Kelly has since tabled a Stage 2 amendment which, if approved, would see the result of any future plebiscite only declared valid if "a minimum of 50% of the total number of persons entitled to vote in the referendum" do so.
The SNP have claimed such a rule would only encourage potential No voters to stay at home if it looked likely the Yes campaign could win.
Mr Kelly’s amendment is not official Scottish Labour policy.
A party source told The Scotsman: “Any decision of such importance must be, as far as possible, the decision of the people who will be affected by it.
“If less than half of the electorate decide the fate of the nation then it is very hard to see that decision as the settled will of the people as a whole.
“What we’re seeing is desperate manoeuvring from the SNP. This proposal has been put forward to ensure democracy is carried out as properly as possible, not to deny it.
“More and more it seems the SNP are panicking in the face of their separatist claims being undercut by the prospect of a radical and transformative Labour Government.”
SNP MSP Angela Constance said the Kelly amendment was similar to the notorious 40 per cent rule imposed on the 1979 devolution referendum.
“Labour refuses to recognise the clear democratic mandate won by the SNP in 2016 to give people in Scotland a choice over their future," she said.
“Now they are putting forward wrecking amendments to the Referendums Bill to scupper a Yes vote and once again stand in the way of Scottish democracy.
“It is inconceivable that a new referendum on whether Scotland should be an independent country would not be much higher than 50 per cent. In 2014 it was 85 per cent.
“This amendment may on first reading seem reasonable, but it is a wolf in sheep’s clothing. It’s not just that it is unnecessary - its only purpose is to encourage a boycott of the poll if it look like Yes is going to win.
“Not since the devolution referendum of 1979 - where Labour MPs put forward the notorious ‘40% rule’ which meant that the Yes vote was scuppered have Labour been so guilty of such a brazenly anti-democratic act, in a last ditch effort to maintain Westminster control over Scotland.
“People in Scotland have the right to determine their future. This anti-democratic wrecking amendment must be withdrawn.”