The genuine Fiat manual shows a pressure bleeder, but that could just be their standard practice, not 'necessary'.
Running the ABS pump with air in the unit might get it all upset, as it relies on pressure/no pressure to sense and work.
Bleed at each union first.
Start at the master cylinder, follow the pipe nearest the bulkhead to its union at the ABS unit. Wrap a rag around that union and loosen it. Get helper to gently push the pedal until fluid leaks inot the rag without air, tighten the union.
Repeat for the other pipe from the master cylinder.
Now do the same for each of the output unions in turn. That should hopefully remove all the air from the ABS unit.
Now repeat at each wheel.
Often bleed screws will draw in air past their threads, to be passed out through the bleed pipe, giving the impression of air in the system.
If you can get the bleed screws out, wrapping the threads with PTFE (Plumbers) tape can help seal them.
Get helper to apply pedal pressure, then open bleed screw, but only for a short time, so pedal does not sink all way to floor. Snap bleed screw shut, allow pedal to return slowly, then apply pressure again. This encourages air to be expelled, and none to be drawn in but does require good teamwork with your helper.
If still air in system, try to raise car so reservoir is highest point.
Attach pipe to furthest bleed screw and open enough to allow fluid to flow slowly. Leave as long as you dare, or necessary, to allow air to naturally flow through.
If you think air is trapped between master cylinder and ABS unit, try this.
Remove one set of front pads.
With help, pump piston out of caliper as far as it will go without falling out. Lots of care needed here.
Allow fluid to settle. Then push piston back into caliper, to push fluid back and expel air into master cylinder. (This works a treat with motorcycles too)
