I have seen similar questions about the missing Suite bar for SharePoint 2013, but in those cases, it was missing for all users. For me, it is missing for only two users. All other user can see it just fine.
I have SharePoint 2013 Enterprise, a fully provisioned User Profile service, search, etc. Everything is working properly except for two users. They can't see the bar. They are using IE 8, but I have requests out to them to try other browsers. They have Windows 7.