Use a proper layout managers (or multiple) next time. BorderLayout, FlowLayout, GridLayout, they all know how to handle resizes of the parent container. But it seems like you have used a null layout manager and are calling setBounds directly. That won't resize your controls, no.
As for which layout manager is best, you'll have to experiment. Check out the
Java tutorial about it. Don't be afraid to add a JPanel with a different layout manager to some JPanel. Nested panels with different layout managers is very usual in AWT and Swing programming.
Oh, and moving to our GUI forum.