I think it would be all in how you presented the offer.
Golf clubs seem to be a boys school of relative wealth and I know that I would like nothing more than the prestige of someone cleaning my car whilst I enjoyed a round.
I would go in with a well thought through portfolio and cover letter, good quality business card and I would ask if there would be an opportunity to offer his clients an on site valeting service.
I would explain to him how it could be mutually beneficial as it would be one more service from his point of view and you would get paid to clean the cars.
People are at the golf club for at least a whole morning.
I will stick my neck out and say that for a external wash with pure water rinse I would want to see £10.00 on a small car, £12.50 on a medium and £15.00 for a large vehicle.
If you present it, your van and yourself why shouldn't the managers be interested.
Rob
