Looking at your image of your layers it looks to me like you are wanting to create your own texture map for a 3d model.  If that is the case then here is how I do it.

Firstly before you do anything else duplicate your original layer then turn its visibility off.  This preserves your original image so you can return to it if you mess things up.

I then make a 'flats' layer which is a flat coloured layer that allows you to make instant selections with the magic wand of any of the parts of the texture map.  I do this by using the magic wand and clicking on the white part of the copy original texture map and then inversing the selection.  I then create a new layer (shift+ctrl+n).  With the selection still active I paint a flat coloured layer on the whole selection.  This now becomes my selection 'template' for all texturing work.  I then move this layer below the copy original.

Next using the magic wand on the texture template I select the part of the map that I am going to work on.  I then make a new layer from this selection (shift+cntrl+n).  I then paint on this layer.  Any corrections that need to be made to levels, clour balance, contrast/brightness etc are then done with an adjustment layer>clipping mask.

Keep repeating the above instructions for any other changes to the copy original texture map using the selection template for quick selections.

A bump map needs to be saved out as a separate image file if it is to be used in something like Poser.  Your bump map only needs to be in grayscale to get the high/low information.  I usually create the bump map exactly the same way as described above using the selection template, then turn off the visibility of all other layers when it comes time to save it out to a new file.

In dreamer101 and Quests post above the Layer via Cut and the shortcut cntrl+j are the same thing.  The reason that I don't generally use this method is that if you make a selection on your original image and cut this selection to a new layer and only partially paint on this new selection layer then if you make any level, curve, colour balance etc changes to your original image then the un-painted part on your new layer will not reflect those changes.  Correcting this by erasing can be difficult if you used a soft brush in your texture painting.

These tips work for me, others will have their own way of doing things.  Try the suggestions of the other responders here and find the one that best suits your needs for your current project.

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