I'm not so much as a beginner as I am a guy who has forgot most of what I learned over the years. Anyway...

I started out a drawing by importing a bitmap then putting different objects on top of the bitmap on multiple layers.

My problem arose when I tried to create a similar drawing. I deleted
the original bitmap then pasted in a new one. The problem is all the
objects are underneath the new bitmap instead of on top. i.e. you can
only see the bitmap not the objects.

How do I organize the objects (or layers)?

You can always send the bit map to the back. if you cannot see the frame for the bitmap : Command line: TFRAMES  toggles all frames on and then Command Line: TFRAMES toggles them off. Select the frame of the bitmap and then send to rear by Draw order toolbar.  Or you can place the bit map on it's own drawing and then x-ref it into your drawing and then select the x-ref and select that to go to the back.  Hope this answers your question.

Thanks.  I'm using AC2010 so it's actually on the modify menu now, but thanks for pointing me in the right direction.