What does this mean? When you play the open B string there is fret buzz. Is there fret buzz when you play the C, a half-step up.? Or a C# or D? If the buzz is only on the open E string, then I'm still not 100% certain the nut slot is cut too low but it becomes more likely.
Very possibly. I'd like to see the experiment I suggested, which is basically a method of measuring the heights of the individual frets above the fingerboard. But if you don't have feeler gauges then you're guessing and I'd guess you're not sure you want to pay a luthier. In that case, it might be interesting to put one or two tiny pieces of household aluminum foil between the B string and the bottom of the nut slot. That's likely to fix the buzz. You still won't know whether it is the nut slot or the fret that needs modification, but you'd have a B string that does not buzz and you will likely forget about all this and just play your bass.