The party wants to ensure no-one is evicted for being unable to pay extra rent because of a cut in housing benefit if they have a spare room.
And to prevent housing associations and councils getting into financial difficulty with arrears, it wants the Scottish Government to stump up additional cash to meet the shortfall.
Labour welfare spokes-woman Jackie Baillie revealed her bedroom tax mitigation plan and said she is preparing a Member's Bill to stop bedroom tax evictions.
Councils and registered social landlords have reported an increase in arrears since the bedroom tax came into force in April this year.
The Evening Times reported in July how housing associations in Glasgow had noticed a big increase, with some estimating arrears at tens of thousands of pounds due to the policy already.
Ms Baillie said tenants and social landlords needed protection now.
She said: "With the impact of the bedroom tax becoming more apparent, it is right that we bring forward a package of measures which will ensure no tenant who is genuinely unable to pay the bedroom tax, loses their home."
Labour said it would be looking for the £50m in negotiations on the Scottish Budget later this year. Finance spokesman Iain Gray said cash can be found in the budget from underspends in departmental spending.
He said: "The financial impact of the bedroom tax on Scottish tenants is £50m.
"But the wider impact is huge with 80,000 households affected, many with children, many including someone with a disability.
"There are no smaller houses for them to move to.
"Meanwhile councils and housing associations face the prospect of soaring rent arrears, threatening cuts to other council services and undermining housing associations' ability to borrow and build."
Housing charity Shelter Scotland has also called on the Scottish Government to make extra funds available. It wants £20m to allow councils to top up the discretionary housing fund to the maximum 150%.
Glasgow received £3m from the UK Government and can add in another £4.5m. It wants tenants in arrears not to be blocked from accessing smaller properties and called for more homes to be build.
Labour and Shelter said everyone who is able to should pay their rent even if they are affected by the bedroom tax.