When it comes to noise, in a car there are any number of possible sources, most of which are dealt with in different ways.
Direct wires to the battery are a good thing. The battery is the most stable power source in the vehicle. Some people will tell you to always chassis ground your equipment, but that is a possible source of noise. Make sure your wires between the battery and CB are not run close to anything that puts out noise. Most car stereos, especially aftermarket stereos, tend to be somewhat noisy, and that noise can transfer into the power leads for your radio.
I have seen some homemade power line filters occasionally, but I have no way of knowing how well they actually worked.
Just because your alternator is powering your car does not mean it is working correctly. The way it is designed it has essentially a built in backup system. An alternator generates three separate AC signals that are converted to DC separately. If the circuit for one of those phases fails the car will likely not notice the difference, but it will generate noise. If you hear this noise through your CB the alternator is, at best, running at 2/3 maximum capacity, and possibly only at 1/3 maximum capacity, and in either case those will be its limits. An alternator running in this state also has the effects of putting broadband noise both in the vehicle's electrical system, and actually broadcasting said noise into the airwaves as well. If you hear alternator whine you should consider getting your alternator replaced sooner rather than later. Sometimes an alternator can run with a single bad phase for years, and others it will completely fail within a week or two.
If you are getting fuel pump whine, that can usually be fixed by putting a small capacitor across the positive and negative power lines as close to the fuel pump as you can get.
If you have LED lights, they make power line filters for the lights, but they are generally very noisy in more ways than putting a signal on the power line, especially the Chinese made aftermarket HID lights. Some are filtered better than others so if you are going to put an aftermarket set on do your research first.
The DB