Personally I'd cut the slots down rather than file the base of the nut, but both methods work. On a bass you can use round needle files to deepen the slots rather than the nut files you really need to use to cut a guitar nut. If the nut slots are considerably deeper than now, then you can also file down the top of the nut, then sand it smooth and polish it (masking off the nearby fretboard and headstock for protection. Just be careful to try and achieve a good semi-circular bottom to the slot and not to widen it more than the width of the string.

Only do a small bit at a time and keep checking the height above the fret. Don't go too far! You need to do this with the bottom filing method as well, which makes filing the slot a lot quicker as you don't have to keep slackening and re-tightening all the strings when removing and replacing the nut.

You'll then want to run some medium and fine grit paper through the slot and you can even use something like brasso for a final slot polish.

But only adjust the nut once you've 1) adjusted the neck relief for a very small amount of concave bow and 2) adjusted the saddle heights for a playable action on the fretted strings. Only then will you be able to accurately judge the string height above the 1st fret.