For solo playing, decide what instrument you want to play bachata on. Although bachata originated as guitar-based music, it also works well on piano too. This is because bachata has a strong foundation of chord playing and chord arpeggios, which are well suited to piano as well as guitar. A bachata band might include two electric guitars (lead and rhythm), electric bass, bongos and sometimes keyboards, though variations may include acoustic guitar and other forms of percussion.
Locate bachata sheet music. You can often find books containing bachata sheet music from music stores. If it is not in stock, you can order it. Start with an easy song and get familiar with it. You may want to consider viewing a few videos of the bachata style being performed (see link in Resources). Watching the music performed while you listen to it can be helpful because it will familiarize you with the playing style.
Play with emotion. If you want to improvise your own bachata, pick a minor key to play in. You can play bachata in major keys, but the minor sound works well for the musical style. Use a lot of chord arpeggios (broken chords) in the melody of the song. Play with an array of dynamics ranging from playing notes softly to crescendos that culminate in explosions of emotion. To play bachata effectively, focus on practicing the sweeping arpeggios smoothly and with the passion the music requires.