We do not apply the word similarly to our everyday "commuter" or "utility" cars. We don't say, "I'm taking my beater car to get some groceries," we just say, "I'm taking the car to get some groceries." So, while the etymology of the word is the same for both bikes and cars, the meaning and usage seem to be quite different.
My suspicion is that there is a cultural assumption that very new, expensive, custom, or high-performance specimens are the norm for bicycles, but not for cars. This, of course, is not true. There are far more "beater" bikes around than there are new and expensive bicycles. So, if the "beater" is in reality the norm, why make the derogatory distinction?
What are your thoughts? Do you refer to your commuter or utility bike as a "beater"? Would you be offended if someone referred to your bike that way?
Here's an interesting piece at the NYT about "beaters."