Remember also that no fretted instrument can ever be perfectly in tune as they have to obey the laws of,"Even Temperament".We as listeners have become accustomed to the the compromise over the years so so long as the intonation on the instrument has been set up correctly for the gauge of strings it's not normally an issue.
I would check if you are bending the string a little when fretting also. I see this a lot especially in people that don't normally play bass. You should post the song though and maybe people can help more. If you have the file without bass I can play something and send it to you to check for sure. cam