It's been my experience that those signs (which are called edge-lit signs, btw) are usually illuminated with an LED strip. I've never seen replacement strips, but you can probably locate one with a little googling.
But if you have the sign in your possession and the bulb burned out, I'd take the burned out bulb to an electrical supply house and have them tell you what kind it is. If they don't have a replacement, they can get it for you.