Its your CV joint, not the axle bearing. The axle bearing is a sealed unit inside the steering knuckle and does not have a rubber boot, and its usually called a wheel bearing. The CV joint has the rubber boot.
If one side goes, the other follows very soon after. Our 97 Accord lost both outer boots within two months. Once the clicking starts, the joint is ruined.
Retail cost on the axles runs $500 for one side and close to $600 for the other, new. Remans from Honda cost about half that. Remans from some parts stores cost a lot less but in my experience are not worth having even if they were free.
New axles from China are available for a little more than the cheap remans and are pretty good. Considering the age and miles, I'd recommend that you go this route, EMPI are the best. Should be about an hour per side for labor, unless you get New Honda axles, then double that as they come un-assembled.