I am going to be buying a new bass soon, and I was wondering if I could put the low B string from a 5-string on my old bass which is a 4-string. It would be tuned BEAD.

My question is, would I have to adjust the bridge or adjust any part of it so it will work on there?
You'd have to tighten the truss rod a bit, but people do it, yeah.
Quote by corduroyEW
Cheap amps are "that bad". They suck up your tone like cocaine at Kate Moss' party.

I am Michael!
You may also need to adjust your bridge for intonation. A guitar tech can help with that.