If chemical bonding is quantum mechanic, is saying they bend and vibrate like springs wrong?
That's a good question, but remember, an analogy is just that: comparing dissimilar things on the basis of structure or function. Though there may not be a physical similarity, the analogy is effective in describing what happens, and can even be used to calculate outcomes, within limits.

In a similar way, the concept of a mass and a spring are used to describe an electrical R-L-C tuned circuit. Both have resonant frequencies and other properties that can be calculated from the physical properties of the components.

One of the difficulties in describing quantum phenomena is that until the physical properties are measured, they may be indeterminate. An electron is not in a specific place, but has a probability of being detected in a specific place. So though the analogy is not physically comparable, it helps understanding of the chemical bond, and can even produce useful results, such as IR spectra, and its use is valid.

This begs the question, though; perhaps there is another analogy that you might find more useful... Any suggestions from others are welcome!