I freedive at Catalina all the time, although spearfishing isn't my main activity.
I gather from my hunter confreres that they often start seeing white sea bass and sometimes yellowtail there around May for maybe a couple of months. Later in the summer the action tends to move to other of the Channel Islands.
I've dabbled a little in spearfishing at Catalina in winter, concentrating on kelp bass, also known as calicos. Although these aren't the big impressive trophy fish of WSB or yellowtail, they are quite tasty and many people view them as even more of a challenge to shoot because they're very skittish.
There are a lot of hunters on Mark Barville's
freediver list
who are at Catalina all the time and can give you more info.
I tend to concentrate on
photography
when I freedive (in fact the top picture on my home page is a typical kelp forest at Catalina).
Good luck!