You still need an invitation to use Google Inbox, and so far the service has only worked with Gmail addresses. That's about to change, with Google beginning tests to offer users of Google Apps For Work access to Inbox as well.
Google says it will begin trials for Apps users (who run on their own company domain rather than using a Gmail.com address) next month (March 2015). You can apply to be part of the trial by emailing [email protected] from your work account — you have to be an administrator for this to work. Google says that only a limited number of companies will participate, and that it will "work closely" with those early testers.
Let's build a new work Inbox together [Official Google For Work Blog]