clippers and clamper wave form
First, are we talking about a clipper or a clamper?
A clipper uses a diode to remove part of the signal. Whereas a clamper shifts the signal up or down.
I've often heard clippers called "clamping to a supply," which is why I ask.
If you're talking about a clamper, a shifter (also called a "dc restore"), it is important that the capacitor (clippers don't use capacitors) be able to charge to the peak and hold it, as that's where the shift is coming from. It's making things look like you have a battery in series with the signal. If the battery isn't charged, then you get nada for a shift, and the diode kills your signal. But if you get the cap charged, all you get is a signal shifted by the dc bias you mentioned.
Here's a trick to "getting" the clamper. The arrow of the diode shows you which way the signal will be pushed, while the dc bias shows you how far the push. ...assuming the capacitor gets charged and stays.
Also, a rule of thumb is 10x. Make sure the cap discharges (there is always a load, remember) slower than your signal's period (1/f) by 10x.
However, bear in mind that the above is just off the top of my head. Clampers were confusing to me too, but then I figured out the above, which I hope helps a little.