Giving evidence this week to the parliamentary communities committee, the Association of Scottish Colleges suggested the FE sector should be exempt from the legislation, as is the case in England.
Both the ASC and Universities Scotland want the Bill to allow the Office of the Scottish Charities Regulator (OSCR) to pass its monitoring function on to the funding councils to avoid duplication. The university body says its members already have to undergo 17 separate monitoring and audit checks.
The ASC fears that the new regime "may create unnecessary and costly additional financial and staff time burdens both for colleges and for OSCR".
Its evidence states: "This could have the effect of diverting resources away from the delivery of education and training to the 500,000 students that Scotland's colleges serve each year. It would also conflict with the Scottish Executive's desire to reduce unnecessary bureaucracy in the public services."
The two bodies have written to Malcolm Chisholm, Minister for Communities, who is responsible for the Bill, stating: "Both universities and colleges are subject to rigorous external audit processes, and their financial accounts are open to inspection by Audit Scotland."
Imposition of separate accounting requirements for OSCR will be "costly and otiose", they say.
The principle of "proportionality" in the Bill could also hit their members, they say. This will require multimillion pound charities to be subject to more stringent information requirements than smaller ones, which would have an impact on the larger FE and HE institutions.
The letter suggests that these "unintended and unnecessary consequences" could be avoided by preserving the existing mechanisms for holding colleges and universities accountable.