Tru-Oil (which I don't believe we have here in Canada) is polymerized linseed oil. What this means is that it's been heated in an oxygen-free environment to give it the properties of drying quicker and harder than plain old linseed oil from the flax plant.
Tru-Oil may have a little bit of metallic driers added to it, I can't be sure not having used it. I have used polymerized tung oil (same idea, different oil) from Lee Valley, and it's got a little bit of drying agents added. Without the drying agents, these finishes are all-natural products (but look, don't eat the stuff or anything.)
Poly oils will give you a "natural" type matte finish, with a little more protection than non-poly oil. However, any plain oil finish won't give you the protection (from dirt, basically) that a varnish or lacquer would give. On the other hand, it won't encase your axe in a thick plastic coating, either.
I've never tried colouring poly oil, but I don't see why you couldn't add pigments to it. Essentially you've got a kind of oil paint (like artists use) after that. Do lots of testing on scrap wood and take your time, hurrying is for other aspects of life, not this one.
The colour won't have that transparent quality that a real varnish/dye combo would give.
I've used poly tung oil on a few basses and other instruments, but only for refinishing necks. I hate slick-feeling necks, as do a lot of players. Poly oil works well for that.
It's prolly about the easiest type of finish to use, come to think of it.
But, I'm sure Bob Branstetter will be along soon with the REAL voice of experience!
One more thing to consider, especially if you're a cheapskate like me: poly oils ain't cheap. Then again, neither is the bass.