Leaked documents show that election officials would also be forbidden from challenging a candidate if they did not believe they were a woman.
Labour’s minority government under Mark Drakeford in Cardiff was accused of “betraying” women by trying to sneak through the reforms.
The draft of the Bill included a clause to allow biological men to stand on female only quotas designed to ensure half of members of the Senedd, the Welsh Parliament, are women.
Cathy Larkman, from Women’s Rights Network Wales, said: “We know from bitter experience that Welsh Government is not listening to the concerns of women in Wales.
“We, along with other groups, have been shut out time and again. Unfortunately, the reasons for this are now apparent.
“The government is now intent on driving a highly contested ideological agenda and this is clearly their first step.
“It is astonishing that the government is spending public funds and using a Gender Quotas Bill to promote an agenda which undermines the rights of half the population of Wales.
“It is shameful that they are high-jacking legislation that should benefit women and increase female participation in political life, to embed a toxic and misogynistic ideology.
“We believe that the intention of the Welsh Government is to introduce gender self-identification and put it on a statutory footing.
“We believe this is the first step towards a full self-ID bill which would have serious implications for women and girls in particular as it would impact on single-sex services and spaces such as changing rooms, intimate care, hospital wards and domestic violence services.
“It is unforgivable that the First Minister and his Government, aided and abetted by Plaid Cymru, intend to betray the women of Wales in this underhand way.”
Plans for self-ID caused a public outcry in Scotland when rapist Isla Bryson, who changed gender while waiting to stand trial, was initially jailed in an all-female prison.
Heather Binning, founder of Women’s Rights Network, said: “Redefining the word ‘woman’ has implications for all women in the UK and is both extraordinary and deeply concerning.
“Despite seeing all that happened with gender reform in Scotland – particularly in the case of ‘Isla Bryson’ – the Welsh government seems not to have learned any lessons.
“Attempting to bring gender self ID in on the back of another imminent piece of legislation that purports to benefit women is devious and disingenuous. It must be resisted.”
It is understood the leaked document is not the latest version of the Bill.
A Welsh Government spokesman said: “We are working to introduce a bill to make our parliament more representative of the people it serves, which includes provisions to introduce candidate quotas for people seeking election to the Senedd.
“Our proposed model for quotas is designed to maximise the chances of achieving a Senedd comprised of at least 50% women.
“Work is ongoing on the Bill.”
