It sounds like you either drained the fluid reservoir and sucked air into the master cylinder, or sucked air back into one of the bleeder screws. You should make sure that the tubing attached to the bleeder screw(s) is full of fluid and pointed uphill from the screw. If not, you could have pulled air backwards into the system. Another possibility is that the person operating the brake pedal lifted their foot off the floor before a screw was fully closed. This can pull air backwards past the bleeder screw threads.
BTW if a brake system is properly bled, you should NOT have to pump the brakes to get a firm pedal. When the engine is off, the brake pedal should NOT have 1/2-2 inches of "give" like it does when the engine is on and the power brakes are operating. Assuming that you've pushed the brake pedal several times to drain all the engine vacuum, the pedal should be ROCK HARD on the first push. It should only move about 1/8 inch and then STOP DEAD. It should feel like pushing down on a hardwood floor
Try pushing the brake pedal 10-12 times in a well-bled car with the engine off. This is the pedal feel that you want
Also, I looked in the service manual for my 99 Pro, and the bleeding procedure is the same regardless of whether or not the car has ABS.