I'm sure you're aware of the Doppler effect, which is observed in situations like when an ambulance with its sirens blaring passes you on the road. First you hear the sirens in a certain pitch but as soon as it passes you it suddenly becomes lower in sound. This is not because the siren is actually playing different-pitched sounds (in fact if people in the ambulance will hear the same sound throughout) but is instead due to the difference in speed between you and the moving ambulance.

Whenever the source of sound is approaching you, the sound waves will literally be "squished" to make a wave with higher frequency. On the other hand, if the source is moving away from you, a lower pitch will be observed because the waves will be spread out more. I think this gif will explain the situation better than my words will.

So basically we have established how the Doppler effect works, and how it can be observed in sound waves. Light is no exception as it is also a wave and the Doppler effect can also exist. The only difference is that instead of observing a difference in pitch (which is what humans hear when the wavelength of a sound wave is altered), the Doppler effect in light waves is observed as a difference in colour. Light waves with "low pitch" is seen as red by our eyes, and as the wavelength becomes shorter the colour alternates between the colours of the rainbow to finally become violet.

The joke here is that to see any significant differences in wavelength due to the Doppler effect, you must be travelling at within ~10% of the speed of the wave in question. In the case of sound, you'll be able to hear differences in pitch by travelling at around highway speeds because it is within that approximate amount of 10% the speed of sound. However, 10% the speed of light is pretty damn fast, a speed humankind has not been able to achieve thus far. That is why driving towards a bumper sticker at max speed will not create any noticeable differences in colour, as the speed at which your car is travelling is simply too slow to be significant enough for light.

P.S.- As other fellow redditors have mentioned, the Doppler effect in light (also known as redshift/blueshift) is observed with stars and it is one technique to judge the relative speed at which a certain star is approaching/moving away from us. So it's definitely a useful technique- you just can't use it to judge the speed of really slow things (i.e. everything on the face of this planet ha)