Why do my bass guitar strings not stay on one exact note?

When I pluck a String on my Bass Guitar, it plays the correct Note for about half a second, then it goes sort of out of tune (like it goes half way between the note below or the note above) and then it sort of repeats this process several times so it’s not playing a constant pitch. Any suggestions on how to fix this? Do I need to adjust the bridge or something? Do the Strings need replacing?

Thanks