I would probably try isopropyl alcohol (aka rubbing alcohol). That would probably work on most inks, and I use it when cleaning electronics because it also evaporates fairly quickly with little residue.
If that doesn't work, maybe try some acetone/nail polish remover on the dirty spots, then clean with window cleaner and a low-lint cloth. If the scanner bed is truly glass, and not plastic, it shouldn't harm anything. If you suspect it's plastic, DO NOT try this, as it may lead to clouding of the surface. (Not sure if there are scanners with plastic beds, but you never know.)
For cleaning my scanner I usually use one of those microfiber cloths (dry, and the fuzzy ones, not the smooth ones for cleaning reading glasses). With a little elbow grease they work pretty well at cleaning schmutz off most things.