Floyd-style Bass Tremolo
As far as I know, Floyd Rose has never made a tremolo for bass guitar. However, there are examples of custom designs which resemble the Floyd Rose style.
Above is a bass player that goes by the name of “Foley” and was the bass player for Miles Davis from 1987-1991. The bass was custom made by “A Basses” and the tremolo was built custom by Harry’s Metal Shop in Queens. The builder says:
“I met Foley when I was living in NYC, he was playing with Miles Davis. Foley wanted A blue 4 string piccolo bass w/whammy bar! Not an easy task at the time…that bridge was not an off-the-shelf item, it took many subway trips to Harry’s metal shop in Queens to get that customized bridge right! Foley’s bass is the closest I’ve come to making a guitar….”
Above is Foley playing the bass. Skip to 2:25 for close up shots.
Above is a more recent video from 2014 showing the same style bass tremolo but with a different bass guitar.
ABM Bass Tremolo
At one time, another company by the name of ABM out of Germany made a similar style bass tremolo as shown above. Perhaps you can ask them to custom make you one?
Mystery Ebay Bass Tremolo
Recently, an unknown bass tremolo was found on ebay which is a string-through model.