Add that to the time spent by other staff, local authority officers and a small army of architects, planners, surveyors and other professionals and the total comes to hundreds of hours every term.
Whereas schools were once given the money they needed to employ teachers, buy books and equipment and provide all the facilities children need to learn, now it seems they have to make a case for every penny. Mr Coates calls it the bid culture.
Last term Mr Coates, head of St Christopher's Church of England High School in Accrington, Lancashire, was working on no fewer than 14 documents applying for funds from bodies as diverse as the Department for Education and Employment, Lancashire County Council, the local training and enterprise council, the National Lottery and the Sports Council.The money is needed for the new devolved funding deal for schools, the National Grid for Learning, the single regeneration budget, drugs education and a project on under-achievement among boys.
"Every hour I spend on this is time I could use teaching and running my school, which is what I was appointed to do," says Mr Coates. "It's as if we're not trusted to get on with the job. It's a way of the Government getting us to do what it wants."
Discontent about the bid culture is widespread among headteachers. It has undermined their professionalism, they say, and takes up enormous amounts of time which could be better spent on other things. Schools have to jump through hoops for money that increasingly is being used to fund not just extras but also mainstream classroom activities.
A certain amount of bidding has always been part of deciding who gets what in education. Schools and local authorities have traditionally had to make a case for money for new buildings.
And fundraising in the community is an informal form of bidding which has become more common in the past decade or two, helping to provide not only a school minibus or computer but also basic classroom equipment.
But the bid culture started growing in a big way in the early Eighties when the Thatcher government turned on local government in its mission to curb the public sector. Margaret Thatcher and her ministers believed local authorities were wasteful and inefficient. The aim was to cut their spending and make them more accountable to the ratepayers who funded them. Bidding, widely used in industry and commerce as a management tool, was one solution.
Compulsory competitive tendering, which forced local authorities to put out services ranging from street cleaning to payroll management, was one result of this thinking. Commercial companies and in-house teams were forced to present bids for these services, showing what they would provide and for how much. Amid furious protest, it was the first step in changing the culture of local authorities from one in which money was given out automatically to employ staff to one in which value for money had to be proved in advance.
In schools, the technical and vocational education initiative, funded by the Department of Employment, heralded a move towards an extension of bidding. Aimed at improving standards of technical and vocational education, the scheme involved schools having to present a case for how they could make use of more resources.
The city challenge initiative, spearheaded by Michael Heseltine when he was Secretary of State for the Environment, brought the idea of bidding to centre-stage for local authorities. In the wake of riots in several urban areas, it aimed to improve the lot of young people in the inner cities by targeting resources on specific projects.
"It was very much part of the Heseltine view of the world which saw enormous potential in central government getting what it wanted by putting a pot of money on the table and getting local authorities to bid for it," says local government expert Tony Travers of the London School of Economics. "It was very successful from the Government's point of view."
"From the point of view of institutions involved, there has been a great deal of complaint about the time it takes. But it has encouraged them to work more with other bodies to get more resources, and on balance it has probably been beneficial. But the caveat is that there may be a lot of time wasted on bids which are not successful."
Since the Eighties, the number of initiatives for which local authorities and schools have had to bid has rocketed and Labour seems likely to take the bid culture further. "It's normal business practice," said a spokesman for the DFEE.
A brochure for schools on the national year of reading, which starts in September, calls it a "key strand in the Government's national literacy strategy and its policies to promote lifelong learning. We plan to engage the whole community in a national effort to raise standards of literacy and create a more literate nation."
But when it comes to the funding, it says: "We will be making announcements in February and in May about criteria for bidding for financial support for national year of reading initiatives. Announcements about the successful bids will be made over the ensuing months."
Headteachers understand how bidding can be a useful management tool, but many think it has gone too far. Tamsyn Imison, head of Hampstead High School in north London and a member of several national educational bodiessays her school has been successful in several bids, including raising #163;139,000 from local industry to become a technology college.
"It can involve a lot of time but that could be time well spent if it means thinking carefully about how the money will be used," she says. "But there is a serious question about whether it is fair.
"The bidding culture is a clever way for Government and other bodies appearing to give generously but in fact only giving to a select few. My concern is that it is a way of eking out very little money and making it look as if it has gone a long way."