As long as you don't skip grits, it's fine to use a random orbit sander. That said, I always do the final sanding by hand, with the grain, to erase any telltale swirls (aka pigtails) left by a random orbit sander. If you're not experienced using a random orbit sander, practice first; it's easy to screw things up with powered sanders!
If you set up a work lamp that shines more-or-less parallel to the surface you're sanding, you will be able to see the scratch patterns with far greater clarity than you can using overhead/ambient lighting.
Make sure you finish an ash "test piece" before you attempt to finish your bass; it'll save you from having to refinish your bass if something goes wrong. TruOil is amber in color; don't be surprised if applying TruOil over green dye changes/muddies the color.