Is scratchy tone caused by too much or too little rosin? Or something else? And should I clean old rosin off the strings? My strings are coated with years' worth of rosin. Does that make the tone better?

Clean those strings NOW. Use a moist (not wet) paper towel or clean cloth, then a dry towel or cloth. You won't get it all on the first pass, so do it a second time, or even a third, if necessary. I wouldn't be surprised of you had a pile of rosin dust laying on the bridge. Brush that off with a dry, cheap paint brush, which you should buy to have on hand for this purpose. And with a dry soft cloth, wipe all the rosin from the front of the bass. It's bad for the varnish.
You should periodically wipe old rosin from the strings.
Also periodically draw the bow across a clean, dry cloth. I occassionally draw a tooth brush along the bow hair, very gently.
This is the most likely cause of the scratchiness. If it persists, speak up (I can't believe I said that).

A scrubbing pad works quite well for clearing off old rosin from the strings.

-dh

From time to time the hair on my violin-bow gets all dirty at the frog. I use a sugarcube or/and a tootbrush to clean it off. Works pretty good.

Toothbrush, yes; soft, clean, dry cloth, yes. A sugarcube? Am I missing something in the translation?

No, it works fine. My teacher recommends it. Other unortodox solutions (or probably not) are the blackboard "crayons" on the tuners if they're running too smoth, or pencil graphite if they're too stiff. But that's for ebony tuners, I forgot that DBs have metal ones. Or do they? Argh, I don't have one at home at the moment - can't remember how the tuners look like. I need coffee.

Anyway, the sugarcube absorbs the dirt pretty good, and works wonders in combination with a toothbrush. You have to put plenty of rosin on afterwards, though.

I just had to get 100 posts. Sorry.

Does the sugar cube not go all crumbly?

A paper towel moistened with Zippo ligher fluid takes the rosin of steel strings in one pass.

...Once you light the fluid, that nasty old rosin dust is OUTTA THERE! :)

alchohol syringe preps work great. get them at a drugstore individually wrapped and you can keep some in a gig bag.