While I agree with Chris that springing for the 5er make more sense, there is another option.
Get a set of 5 string strings (wow...alliteration!), discard the G string (or donate it to your favorite stripper...), and just use the bottom 4 strings. You will have to have the bass set up for this adventure: The nut will have to be reslotted for the larger gauge strings, the neck will have to be readjusted for the different tension on it, and the bridge would have to be reset for intonation. A pain to be sure, but doable. You
CANNOT just tune down your standard 4 string set, it just won't work, the strings are too small of a guage to be tuned that low and be playable. They'll just flop around and buzz.
So, I'd just get a 5

.