This is one of several issues that has led MSPs to call on the Scottish Executive to review the 25-year-old legislation covering school transport.
A quarter of the 146,000 pupils entitled to free transport use public bus services.
Aberdeenshire Council told the parliamentary education committee: "A number of parents indicated that they would not allow their children to travel on services which are open to the general public, despite there being no evidence of any problems on the services which have operated successfully in this way for over 20 years."
The council is now being forced to deregister some 280 bus services which, from August, will carry only pupils, but no members of the public.
Angus has also reported "unease" on the part of some parents, although it continues to operate a number of school buses as public service vehicles.
Judith Gillespie, development manager for the Scottish Parent Teacher Council, urged councils not to "pander to such neurosis" on the part of some parents.
Meanwhile, in a letter to Peter Peacock, Education Minister, the committee points out that the current laws governing school transport go back to 1980 and appear "not to be based on issues of children's health and safety or environmental concerns".
MSPs point out that a number of councils have abandoned the age threshold required by statute - two miles from school for any pupil under the age of eight and three miles for children aged eight and over - and have chosen to differentiate when primary pupils move on to secondary. Others have chosen to provide school transport significantly beyond the statutory minimum age.
Angus said it was "bemused and challenged" by the allocation of funding to authorities. Aberdeenshire reported a significant shortfall between the costs it incurs in providing school transport - pound;11.24 million in 2004-05 - and the level of grant it received for this purpose, pound;3.31 million. It wants more recognition taken of the cost of transporting pupils over large rural areas.
As a consequence, the council had to increase its minimum walking distances from one mile to primary and two miles to secondary to two miles and three miles respectively.
West Dunbartonshire says it conforms to the legal requirement that seat belts must be provided in all cars, minibuses and coaches, but not in buses. There was a high level of expectation that seat belts should be provided, but contractors across Scotland have expressed concern at the level of vandalism on secondary school contracts, in particular where seat belts were in use.
North Lanarkshire said that to extend seat belt provision to all school transport would cost pound;500,000, while Aberdeenshire said that such information as did exist from North America suggested that lap belts might offer limited benefits and that three-point belts, if improperly installed or incorrectly worn, could result in increased risk of injuries.
There were also calls for policies on transporting pupils with disabilities and those attending Gaelic-medium classes.
A spokeswoman for the Executive said that Mr Peacock would respond to the committee in due course. "Obviously, pupil safety is of paramount importance for all those involved in school transport," she said.