There are several things you might need to consider before you tune down your bass. If you are talking about tuning all strings down a 4th, ie. BEAD then you will need to use the appropriate strings. Using E A D and G strings respectively won't really have the tension even if you use very heavy gauge strings. If you are going to do this as well you might want to consider having your bass set up when you do it as this kind of change will probably alter intonation and tension. You will also need to make sure that your nut can take the thicker strings.
On the other hand if you are talking about just one string and having tuning like BADG then you can probably get away with using a heavy gauge E string or perhaps a light gauge B string. I personally tune my E down to C on some things and this does create a loss of tension even with heavy gauge strings like 105's but depending on how you play you can get around it. If you are thinking of having your low string tuned down to the low B permanently I would probably just go for using a B string, but once again if you opt for this, I would have your bass set up to counter any tension and intonation variances.
All things being equal though, if you really want to go that low, and unless you are willing to sacrifice the range at the top end, I would probably look into getting a 5 string.