"Maybe" on the nut and bridge. I tried using a 5 string Labella Low Tension Flat set(using only the lowest 4 strings) on my Roadworn Fender P and it worked fine as far as the nut and bridge needing no modification to accommodate the thicker strings. I played it for about 15 minutes and switched it back to standard tuning because I didn't care at all for how it sounded, but setup wise it was no problem. Of course some basses will require the mods you mentioned, but just chiming in to say, not always. I've done the same thing with a MIM Strat, put on some 13-63 DR's and tuned it like a Baritone(B-B) and it worked fine with no mods. YMMV.
Caveat Emptor - and strange but true: even going to a thicker guage regular string set may require a (very) light swipe or maybe even two with an appropriate nut file. Generally only if the thicker guage is a permanent change. I say may require because the slightly raised action at the nut is often acceptable. But if you're picky it might not be. Going down in gauge can be done to a point if the nut slots are cut right (meaning if I didn't cut the slots
So I'm very skeptical that a change as large as BEAD on a regular EADG bass won't give a mile-high action at the nut, even to the point that it bugs the player significantly. Putting it another way, just plan on if going BEAD, it'll mean recutting the nut and possibly a bridge saddle or two That's kind of my motto on that. That way if you don't have to do it it's simply a pleasant surprise. Otherwise, it's a nasty surprise if you do have to recut it on a favorite bass and you don't have the tools etc...
L