Tell them why you're interested in becoming a member and request application information.
1234, Main Street
Boston, MA 02123
<Recipient Address Goes Here>
I heard about <name of business association> through <name of reference>. Our company is an established member of the business community, but doesn't afford me the opportunity to meet with people outside our industry.
In order to broaden my contacts within the community, I would like to become a member of your organization. I'm very interested in getting together on a regular basis with people that share the challenges and joys of running a business. Please send me membership information and any background material you might have. I look forward to hearing from you.
encl: <List of enclosed items goes here>