You're confusing 2 different but related concepts. Blueshift and redshift does depends only on velocity. In the cosmological sense, redshift (the opposite of blueshift) occurs because everything is moving away from everything else due to the expansion of the universe, and so the distance of an object can be calculated based on how much redshift there is in the light. Basically, on a cosmological scale, distance and velocity are connected

The doppler effect you can hear when something loud passes you happens to light too. It would have to be aproaching very fast indeed however to make a red rose appear blue. (Like fast enough to fuse atoms in the atmosphere)

Doppler shift is based on relative velocity, the result of red shift is that stuff which is moving away fast enough to produce red shift is far away by virtue of being fast and stuff and stuff that is blue shifted needs to be far away or it will collide with you very quickly or just pass you by. The relative velocities required for doppler shift are pretty high speeds so you normally observe it in stuff that's far away, but distance isn't really a requirement for doppler shift to happen or be observed.