The proposals could see visitors to Edinburgh charged an extra rate during the August festival season, with proceeds ring-fenced for cultural activities.
It has previously been estimated that Edinburgh City Council could raise £10m a year by charging £1 or £2 per hotel room per night.
But the BHA said it hoped the new SNP-led Government would create ‘certainty’ for businesses by dismissing the notion.
Nicola Sturgeon’s party swept to a historic third victory in last week's elections, but fell two seats short of an outright majority.
Willie Macleod, executive director of BHA Scotland, said: “While our industry is resilient it is not immune to competitive pressures.
“BHA Scotland has high expectations of the new Government in providing support to the industry to achieve greater growth, improved productivity and enhanced skills, particularly for young people.”
Hospitality directly employs 256,000 people in Scotland, up 15 per cent since 2010, and contributes £4.6bn towards the economy.
The BHA also called on the Scottish Government to reduce air passenger duty, reform business rates, and acknowledge the impact of the Living Wage on businesses.
In Wales Labour fell just short of an outright majority in the Welsh Assembly.
David Chapman, executive director at BHA Wales, said he would work with the new Government to widen the ‘recognition of hospitality’s crucial role as a powerhouse in the Welsh economy’.
The hospitality sector accounts for more than 135,000 jobs in Wales, including many in rural and coastal communities.