It's worse than the doppler effect; it's both the doppler effect
and time dilation, compounded.
I mean say you are approaching a sequence of sidewalk squares, each 1 meter in length. If you are going 1 meter/second (walking speed), you see one square pass you each second. If you are on a bicycle going 10m/s, you see 10 squares passing you each second. So to see the squares even going by at the same 1 second each speed, your internal "framerate" would have to be 10x as fast, making your clock need 10 seconds for 1 second of the rest of the world. To make things look like "slow motion", you'd have to think each line is going by at say 10 seconds, your internal clock would need to be 100x faster - you'd need 100 of your seconds for each 1 second of the real world. Or put another way, you spread out 1 second of "world time" into 100 of your local seconds.
But this is opposite time dilation - if you start moving quickly,
more "world seconds" get crammed into
your one second - not less! So to exaggerate, 10 real-world seconds get crammed into 1 of your seconds. That is - the world ages 10 seconds for every 1 second you age. This is the opposite effect of what is portrayed, where the fast entity ages more than the rest of the world.
So if you were moving
that quickly, your internal "framerate" would have to be some ridiculous multiple of your speed, to result in you perceiving things as being in slow-motion.
Also, it's not even considering length contraction and blue-shift/red-shift, which is also all sorts of fun