The ONLY way I've ever seen/heard/done to manually bleed the brakes is exactly like what the workshop manual is stating. You need to do it in the order presented or you'll be defeating your purpose. If you open the bleeder then pump, it will draw air into the system through the bleeder valve.
The only other thing I'd add, is to put the end of the clear vinyl tube into a clear bottle, by submerging the end of it in a little bit of brake fluid (have a small amount already in the bottle). By doing this you ensure air won't be sucked back up in the line for whatever reason. It is also a collection bottle for the old fluid so it can be disposed of properly.
Let me see if I can add a little bit of context to the shop manual's procedure:
- Connect a transparent vinyl tube to air bleeder valve.
Straight forward. It is also a good idea to crack the bleeder open, then reclose it, prior to putting the vinyl tube onto the bleeder. It's just easier to get it ready for bleeding as the tubing will not be in the road.
- Fully depress brake pedal several times.
Once the brakes are hard to press, then hold the pendal down. By doing this, you are pressurizing the system. If the system is not pressurized, there's no real way for the fluid to come out.
- With brake pedal depressed, open air bleeder valve to release air.
Whomever is helping, should keep the pressure on the brake pedal. This keeps pressure in the system. If you don't do this, you run the risk of sucking air back into the system during the next step. Once the bleeder is opened, the brake pedal will go to the floor.
- Close air bleeder valve.
So no air will be drawn back into the system.
- Release brake pedal slowly.
To allow the master cylinder piston area to refill with fluid.
- Repeat steps 2. through 5. until clear brake fluid comes out of air bleeder valve.
"Clear brake fluid" means two things. First that old fluid is removed. It becomes dark green in color (if not exactly green, it will be dark/murky) over time as it absorbs water. You're looking for the clean new fluid which you've put into the master cylinder at the start of this operation. Secondly, if the system has been opened for any reason (ie: new caliper installed; brake line replacement; etc), you'll have air in the lines. You'd be looking for any air which might be in the system to be removed.