The Bananarama version was off their 1986 album True Confessions, and their cover of "Venus" would also go on to become a #1 hit in the U.S., one of three top 40 hits for the band ("Cruel Summer" (#9) and "I Heard a Rumour" (#4) were the other two). Amazingly, "Venus" did not hit #1 in the U.K., in spite of the band's success in their home market -- in the U.K. Bananarama had 25 top 40 singles, making them the most successful all female act ever.
Bananarama was formed in 1979 by Siobhan Fahey, Keren Woodward and Sara Dallin. The band was known for its lite pop songs and the lack of harmonizing (the three singers typically sang in unison). Sadly, creative tensions led to Fahey's departure in 1988; she would go on to form Shakespears Sister. Jacquie O'Sullivan replaced her in Bananarama from 1988 - 1991, but when she left, the band continued on with two lead singers (which is the status to the present day).
While Bananarama were not critical darlings, they did release a bunch of solid 1980's dance pop, including "Venus:"
Amazingly (love the internet), I was able to track down a video of the original version, by Shocking Blue (Note that the volume on this one is a little loud):
Cool trivia fact: Siobhan Fahey was married to Dave Stewart of Eurythmics from 1987 - 1996. (Man, that guy was everywhere during the 1980's.)
Bananarama's "Really Sayin' Something" (with a g and Fun Boy Three) was posted on ERV in October 2015.