Check the supply list of needed items that was sent with your first packet. This is determined by the amount of time you put into raising the money. When approaching civic groups or groups who make board decisions, allow three months minimum . The first month you make your request in person or in writing, the second month they act on it and the third month the check is in the mail. Foundations have specific time lines such as grants given annually or semi-annually.
Corporations range from immediate to lengthy board of directors' approval.
Don't just open the phone book and send hundreds of letters to people you don't know. Before sending the letter to people or businesses you do not personally know, call and tell them it is coming and why it si being sent to them. Or, after sending the letter, follow up with a phone call to see if they have any questions. Both methods get results. Doing nothing gets nothing.