Firstly, imagine forcing the power through your heels when you're lifting, not the front of your feet. Don't worry about falling backwards because you want, but placing the emphasis over your feet will inherently make you lean forwards. By bracing your core you're essentially tensing/flexing your abs and lats. Brace those abs, pull the bar in to your shoulders (thus engaging your lats), and slowly lower yourself until you hit parallel. Now to avoid bouncing, you lower yourself to parallel and then hold it there for half a second, then begin driving through your heels to push back up, all the while keeping abs and lats engaged.