Hello , Do you think twitter direct message work for approach other twitter followers for promote your business ?
For me it doesn't worth, because I have sent many personal messages for promotion of my website but not a single positive response.
You cannot force your offers to your followers. If you provide value to them, they would definitely follow you. Be careful while sending mass direct messages as your twitter account would be in risk, if people start reporting. Instead, get more followers and tweet regularly. Update your site content, etc. That should work.