Can this be done?
http://www.ebay.com/itm/6PC-FLEXIBLE-NEON-LED-MILLION-COLOR-INTERIOR-LIGHT-KIT-/280602064035?pt=Motors_Car_Truck_Parts_Accessories&vxp=mtr&hash=item41552fb4a3

PDF Downloads
As a Pro member, you will gain access to download any Instructable in the PDF format.
You also have the ability to customize your PDF download.
Here's an LED ribbon light that's intended for "in home use" and its a lot cheaper.
Without really seeing photos of your bar and shelving its a little hard to suggest specifics. Glass shelves and wood shelves would require different lighting solutions. The most cost effect solution I would think is using spotlights. You can get them in various intensities, in track mounts, wall mounts and individual units that are more customizable.
I'd be glad to help further, but I think you need to upload a photo or two at this point.
You can use a "wall Wart" 12 volt power supply for most of the low amperage car accessories.You would need to cut the end off and splice it on to the power connector. Another thing to use would be an old salvaged computer power supply.
I kind of like the ribbon lights thing. I didn't know that stuff was available.
What would work best for your needs would be Christmas lights which most stores now have on close out sales. I saw some for 70 % off the other day. You can get white ones or probably solid color ones.
Another alternative is the small cold cathode lights that are used for computer case modding, something which is dieing out in popularity.
Here is a company that has all kinds of lighting stuff for computers.
http://www.svc.com/lighting.html