I got this bass for a steal, but it had an ugly paint job so I decided to sand her down. I got down to the wood and realized it looks like alder - huge plus! On the other hand, I really don't know what I'm doing. It appears that there is a laminate or underpaint on the top. Not sure how to get it off! What is it exactly?

Once she's stripped I'd like to leave her bare with maybe just a matte varnish or something. Should I treat the wood with a filler or anything before doing this?
Well there is a laminate and probably also an "undercoat". The laminate or veneer is added to the top of many multipiece bodies so you dont see the glue joints when painted. You can see on the edges its a 4 or 5 piece body. The "undercoat" is the sanding sealer they put on before paint. If you haven't gone through that to the wood yet then you won't need to do any grain filling.

IMO that body needs to be painted again, if you leave it like it is and clear it, it has that awful area around the forearm contour. If you sand further and remove the rest of the veneer you will see all 4 or 5 distinct body pieces. If it looks good to you that way then go for it. Just not my preference.
Thanks for the clarification. How would I tell whether I've gone through the sealer?

How thick do you suppose the veneer is? Would I be able to sand it off or would there be an easier way to get it off if I wanted?
Is pretty easy to see when you gone through the sanding sealer, basically instead of white dust you will get saw dust. The veneer will be super thin...you can see it right there on the top, its the lighter colored area across most of the surface of the top. You can see it ends right there on the arm contour where you see the different colored wood. It looks like you have probably already burned through the sealer right there on the angled line of the arm contour.