[Efthreeoh]

I believe to fix things, you need to first understand how they work.

Based on your description of how you tried to bleed the brakes, it's obvious you don't understand how they work. So first, a little physics. The system is based on Pascal's principal where force can be transferred through fluid. Force can be transferred through the fluid because fluids basically don't compress very well, so pressure is easily created and the pressure of the fluid transfers the force. The brake system uses five (5) hydraulic pistons to transfer the force using the fluid. One piston sits in what is called the "master" cylinder and the other four (4) pistons sit in what are called are "slave" cylinders, one (1) at each brake caliper at each wheel. When you push on the brake pedal, which is connected to the piston in the master cylinder, it compresses the brake fluid and pushes it through the small brake pipes and hoses to compress the fluid stored in each of the slave cylinders and pushes the piston in each brake caliper. The brake caliper piston then pushes one of the brake pads against the brake disk, which clamps both brake pads on the disk. This is action of transferring the force from your foot from the master cylinder to the calipers.

Now to your problem, when you pulled the fluid out of the mater cylinder reservoir and did not preplace it, you just pumped air into the system to push the old fluid out of each caliper. Filling the reservoir with new brake fluid BEFORE you start bleeding the old fluid out at each caliper then uses the new fluid (rather than air as you did) to push out the old fluid of each caliper. Pulling the old fluid out of the master cylinder reservoir and then filling the reservoir with new fluid as the first step just speeds up the process by replacing most of the old fluid before it get cycled through the system and out the calipers. Your brakes are now spongey because you have air in the brake lines and calipers. Air is highly compressible (as compared to fluid), so pushing on the brake pedal is just compressing the air in the brake lines.

So as others have said, you need to start over and bleed the system the proper way using the correct technique. While a pressure bleeder would help greatly here, you can use the pump method (if you have a partner to pump the brake pedal) to bleed the brakes - if you use a buddy to pump the brake pedal try to not bottom the pedal out because it can, if bottomed repeatedly, possibly damage the master cylinder. Now, the only unusual issue you may have trying to restore the function of your brake system is you probably pumped air into the ABS valve body, which is not a good situation. The ABS valve body is a device that prevents the brakes from locking the wheels (tires) and the car skidding by rapidly varying the brake line pressure to each wheel from your panicked foot slammed down on the brake pedal. Bleeding the air out of the ABS valve body is not easy and usually requires cycling the ABS function (rapidly opening and closing the valves in the ABS valve body), which is accomplished by using a computer to communicate with the valve body to cycle it. To cycle the ABS valve body, you need a device that runs BMW diagnostic software. You can learn about such diagnostic software in the coding subforum.

About brake fluid... (I know I'll get flamed here). Brake fluid is a chemical produced to a engineering specification. All BMWs use "DOT 4" brake fluid; "DOT" meaning (US) Department of Transportation. So any brake fluid that is rated as meeting DOT 4, regardless of its price, is completely adequate for your car. ATE is just a brand of brake fluid. NAPA DOT 4 brake fluid will work just as good as ATE, but just isn't as cool to use because it doesn't have a designer name.

The last bit of advice is consult the BMW Newtis.info website to review BMW repair procedures. Sorry for the long post, but hopefully it helps you get the brake system operating correctly.