This is a common problem - before multiplying speed by -1 you need to place the object within safe bounds by adjusting the relevant x or y coordinate which may require splitting your conditions up.  e.g.:

Code:

if(ballX < padX){
  ballX = padX;
  dx *= -1;  // shortcut for 'dx = dx * -1'
} 

It's actually a little more tricky than I first thought since you need to know which direction the ball is coming from and that can get tricky if the ball is travelling at high speed, especially if your rectangle is small.  Here's a function that bounces a ball off a rectangle:

Code:

// Assuming a rectangle using rectMode(CORNER)
// Note that this will fail if ballSpeed is high enough to place the ball beyond the far boundary of the rect on collision
void rectBounce(Ball ball) {
  int rectRight = rectX + rectWidth;
  int rectBottom = rectY + rectHeight;
  // check that the ball is inside the rectangle
  if(ball.x > rectX-ball.radius && ball.x<rectRight+ball.radius && ball.y > rectY-ball.radius && ball.y < rectBottom+ball.radius){
    // If it is check which boundary it has hit
    // Note we don't use the radius offset here as the ball is already inside the rectangle
    if(ball.x < rectX) {
      ball.x = rectX-ball.radius;// place at appropriate side
      ball.vx *= -1;
    }
    else if(ball.x > rectRight) {
      ball.x = rectRight+ball.radius;// place at appropriate side
      ball.vx *= -1;
    }
    if(ball.y < rectY){
      ball.y = rectY-ball.radius;
      ball.vy *= -1;
    }
    else if (ball.y > rectBottom) {
      ball.y = rectBottom+ball.radius;
      ball.vy *= -1;
    }
  }
} 

This takes a ball object as a parameter, but it should be simple enough to adapt and assumes variables have been set to define the rectangle (or 'bat' in your case) dimensions.

Mind you I suspect this is a FAQ and you may find better solutions if you search; either here or on the wider net.