Establishing a good hand frame will help the most with intonation. By hand frame I mean that your fingers should be able to maintain the same basic shape for all 4 strings. Of course minor adjustments will be necessary for low 2’s, high 3’s, etc.
Keeping your fingers hovering just above the strings will also help. Once you have found the correct location of a note, you should be able to hover right above that note so that it is ready when the note comes back again.