Connect VBRIDGEA to +5V and GNDA to Ground. OUT-A and OUT+A will then give you a voltage of about 60 millivolts times the sine of twice the angle. Similarly for bridge B you will get the cosine of twice the angle. With those voltages, and some signal conditioning, and some math, you should be able to determine angles in a range of +90 to -90 (half a rotation).

If you want to sense an angle you might be better off using a magnetic rotary encoder like the AS5040 which will give you a digital output:

http://www.austriamicrosystems.com/eng/Products/Magnetic-Encoders/Rotary-Encoders/AS5040