Back in November, Twitter announced a new way to speed up customer service for business accounts. They introduced new features such as quick replies & welcome messages. Over the course of a few months, businesses started integrating these features into their DMs. When Twitter released their API Roadmap, they also released the DM API to the public. This meant that ANYONE could build a DM bot with these new features.
Listed below are multiple accounts, business and non-business, that have DM bots.
Customer Service Bots
Official Twitter Bots