All magic effects have visual/sound effects associated with them, and spells will use the visual effects of their most expensive magic effect. Script Effects have their own visual effects as well, but can take on any other visual effects for spells. Of course, script effects always cost 0 Magicka, so they'll be overruled by any other effects anyway.
That is to say, if Shadow Bolt only has script effects, you shouldn't need to do anything more than open up Shadow Bolt, select the script effect(s) in question, and select "Reanimate" from the Visual Effects drop-down box at the bottom of the effect-details window.
If Shadow Bolt
does make use of non-script effects, it's more troublesome. A traditional solution is to insert the desired visual spell effect in such a way as it's very expensive, and won't do anything at all (For example, Charm 100 for 0 seconds). This isn't viable here, though, since Reanimate can't be done on Self, and the only thing about it you can change is the duration. Theoretically, if you don't mind worrying about conflicts, you could turn one of the magic effects that Bethesda doesn't use (A list can be found
here) into a "Dummy" magic effect that uses Reanimate's visual/sound effects, and put that into your spell with a huge duration.