No, you don't NEED to buy a bench, provided the chair is the right height and you sit on the front edge of it (thus avoiding the temptation to sit against the back). I use a chair frequently when I practice at school because the bench is too high for me in some of the practice rooms.
The proper way to play on higher or lower parts of the keyboard is to pivot your torso left or right (don't twist), so that your butt pretty much stays planted. Sliding on a bench is distracting -- especially if, in the piece you're playing, you switch back and forth from 8va frequently. Then there's the issue of staying oriented on the pedals... Simply stated, if your left arm is running into your body, move your body out of the way, but keep it parallel to the keys.
This is one technique solved by playing scales and arpeggios -- since, in playing them over 4 octaves, you learn how to keep a neutral posture while allowing your hands to play higher and lower.