Try using naphtha to clean the tape residue. It's the main component of Ronsonol lighter fluid, which you should be able to get at a Walgreens or the like (a bright yellow bottle). Butane lighter fuel or the stuff in a Coleman white gas bottle is also OK. Obviously, this stuff is violently flammable so exercise appropriate caution!
You may remember what's going on if you took chemistry. Molecules have a lot of different properties based on the atoms that their built from and how they're assembled. One of those properties is polarity which describes how the electrical field is distributed around the molecule. Some substances like water or ammonia have an uneven distribution and are polar; substances like gasoline or naptha have a very even electrical distribution and are non-polar.
When you want to dissolve something, polar solvents dissolve polar substances; likewise non-polar substances dissolve in non-polar solvents.
You've probably already tried using water to clean off the tape residue and it didn't work, so polar solvents probably won't do the trick. Isopropyl alcohol is a strong polar solvent, but it won't make much progress on the goop.
So, try a polar solvent like naphtha. It should dissolve the gunk. Naphtha is from the same chemical family as gasoline, but it's much less reactive, and less likely to damage your finish.
The polyurethane or polyester varnish on your bass is relatively resistant to chemicals. As you've probably seen on the warning for any cleaner, try naphtha first in a less visible area to make sure that you don't dissolve or fog the finish. If there are cracks in the finish down to the wood, you should be extra careful as any solvent may cause discoloration in the wood. Tape residue is usually just on the surface, so you should be able to get this all cleaned off.
Class dismissed,
David Fung