In Jakarta the people speak Bahasa and Javanese equally. People who have come in from other areas of the country speak their own language plus Bahasa; the Javanese who were born there make Javanese the most common language.
Malay and Bahasa are 90% the same language. Bahasa is considered a traders' language, much like Swahili - a lingua franca that allowed commerce to happen for centuries.
Source: studied bahasa for two years and used to live on Java - amazing, complex place.