From the comments provided by @musicamante, it sounds like you don't have a problem with your setup, but that the strings library you are using has some out of tune notes. This is also suggested by your comment that some other notes are out of tune, but by different amounts. (If all notes were equally out of tune, this would suggest some kind of global problem, such as erroneous pitch-bend messages, or some kind of global fine-tune setting being off...)
I don't use Ableton, so don't know if you could tune individual notes in a sample library, in the way you can in Kontakt, for instance. But to be honest, this would probably be a massive pain in the rear end anyway.
The simplest solution, particularly for a "single-line" instrument like bass is to change the pitch of any out of tune notes. There are two main ways you could do this:
- bounce the audio, then chop up it up to isolate any out of tune notes, then fine tune these notes.
- use a pitch correction plugin: as far as I can tell from searching on Google, Ableton doesn't have a native plugin for auto-tuning, but you can either buy one or download a free one. This would be the only solution if you are using Ableton to play live.
If there are only a few very out of tune notes that you want to change, you could even put these all on one track and just fine tune this track, and leave the other notes on another track using the same instrument.