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The higher up the neck, the sharper the note

Quick and dirty is to "ring" the note by placing your finger over the twelfth fret w/o fretting it and pluck it. Compare this note to the note when actually fretting the twelfth fret. If the fretted note is higher, the saddle needs to be moved back and vice versa. It's a lot easier to do this with a tuner if you have one.
 
Strings are too "short". Make them effectively longer by adjusting the bridge saddles away from the neck, toward the end of the bass body. Might not take much adjustment to get it right, don't go nuts.
this. i just had this exact problem after changing sting gauges. the link for the manual above is good info, but here's my version & how I did it

1) tune the open string you are messing with 1st with a digital tuner
2) fret it at the 12th fret & look at the tuner again. it'll be sharp.
3) take a screwdriver & start turning the screw on the bridge in a way that moves the bridge for that string backwards towards the back of the bass. I had to move mine way more than I initially thought I would. dont be scared you aint gonna break nothin'
4) after a few turns, re-tune the open string again & start over. keep repeating until the open string & the 12th fret are both close. you'll never be perfect, i think thats pretty much impossible even on an expensive quality bass.
5) move on to next string

good luck man. i followed those instructions (that i read about here!) and it worked great. really great.
 
The basics of setting intonation are here in this thread. Compare the open string or its 12th fret harmonic, either one is equally valid*​ if your strings are in good shape (and if the strings aren't in good shape, none of this will really matter anyway) to the fretted note at the 12th fret. The open string/harmonic is your standard, and you need to adjust the fretted note to match that. If the fretted note is too sharp, that means the string is too short; if the fretted note is flat of the standard, then the string is too long.

If the fretted note is sharp, move the saddle away from the nut, retune and check again. Always retune and check again after every saddle move. If the fretted note is flat compared to the standard, move the saddle towards the nut. Some trial and error as you dial it in but after a while you get the hang of it and can do this pretty quickly. No good reason to pay someone to set intonation when you can get a good tuner for so cheap.

John

*​The 12th fret and 5th/17th fret harmonics ARE exact octaves of the open string so there's absolutely no reason to avoid using them in favor of the open string. And, given that they vibrate at a higher frequency, your tuner has a better chance of counting the vibrations accurately (a higher sampling rate as it were) than with the open string.
 
Very good points in this thread. I tend to check the intonation by doing 12th harmonic, fretted 12th. I use a tuner to get it close, and my ear to get it to stop "wobbling" In my experience, a little cheap korg tuner or something isn't enough to get the intonation right, they just seem to vary too much when you hit the note. A strobe tuner is optimal for intonating. Another way is to ring 7/19 harmonics. They should ring off at the same frequency.