How does one get top and bottom bar on Adobe Reader app with recent documents button etc.?
Just tap the document you're reading. (Note, not a long-tap; that opens a different menu.)
From page 5 of &quot;Getting Started with Adobe Reader.pdf&quot; (which downloads with the app):

My PDF documents are in Adobe Reader. Now what do I do?
Tap the middle of the screen once to reveal the toolbars. After a few moments, they disappear until you tap again.