Think first of how you can be of service, and it will come back to you ten-fold. Don't worry about bothering me. I enjoy receiving emails that are personal in nature - this business is all about building relationships. Promote my newsletters in your circle of influence, through your own newsletter, or by forwarding it to friends and colleagues. If you truly enjoy a newsletter and find it of value, give it your personal recommendation - that carries weight with the people who know and respect you.
Online newsletters grow primarily by word of mouth referral.
Help me with that. Thank me for running your article. Tell me how it helped you in your business. That makes me feel good. When you make me feel good, I will remember you positively, and I will want to help you again.