Yep, you're on the right track—mechanical switch bounce is the most likely culprit here. Mechanical contacts don’t just close once—they physically bounce for a few milliseconds, causing multiple rapid transitions that your SR latch interprets as separate inputs. That’s why you're seeing multiple or unstable output changes.
To fix this issue, I recommend using a resistor and capacitor on the input line. A typical starting point is a 10kΩ resistor and a 0.1µF capacitor. This will help smooth out the bounce. Also, make sure the inputs aren’t floating and are properly pulled up or down. That should clean up the behavior of your SR latch.