The answers provided here offer a useful trick, which is to quickly translate into a scale you already know to find the answer. For instance, if you know that
C to E is a major third, then it must be the case that
Cb to Eb is a major third and also that
C# to E# is a major third, too.
It's fine to use this trick when it comes in handy, but it sounds like you really need to drill through your scales. You've got to know them cold. Then this useful trick helps you think faster, but does not become a crutch. Like all tricks, it is only helpful some of the time.
So, Bb to Db is a minor third. That's because in the Bb major scale, Bb C D Eb F G A Bb, we do not have a Db. The major third, Bb to D, is reduced by one half-step, producing a minor third. You can also say that in the Bb minor scale, Bb C Db Eb F Gb Ab Bb, the Bb to Db is the normal minor third that appears. Either way, referring to the scale is the best way to understand it in the long term.