I don't find complete washing necessary before bleaching. Do rinse for a few minutes after fixing to reduce the amount of fixer residual in the emulsion. The more fix in the emulsion, the faster the bleaching will take place, as the fixer accelerates the bleaching process.
I routinely bleach, rinse, return the print to the fix, rinse, bleach again (often the same area, building up to the amount of bleaching I want) in several iterations.
Use a tray bottom or other flat surface at an angle. Keep the area you are bleaching at the bottom if it's just an edge. Keep a hose with running water under and around the area you are bleaching and to rinse the bleached area when it has reached the desired density.
After bleaching as much as you need, refix completely, rinse, treat in wash-aid and wash fully.
Doremus