That's a normal phenomenon known as tramlining, most road bikes do it to some degree, wider tyres seem less susceptible. My first concern if your bike feels really bad would be that the headset or front hub is worn or improperly adjusted, or the frame and/or fork might be bent or cracked. If none of those, you could try changing your tyre pressure - higher pressure may feel more sensitive to road defects but react more directly to your steering input. Also shifting your riding position to put more or less weight on the front wheel can make a difference.