Is this stepper unipolar or bipolar?

The motor I'm using is the M35SP-9: http://www.mitsumi.co.jp/latest/Catalog/pdf/motor_m35sp_9_e.pdf

On the data sheet it says 2-2 phase unipolar excitation, but it only has 4 wires. Is this bipolar or unipolar?

Well only 4 wires suggests bipolar, but the data sheet says unipolar. See this for driving pattern:- http://www.societyofrobots.com/member_tutorials/node/28 One thought though is the case the common connection for all the coils?

Common connection for all the coils?

Yes if the case was common then you would have in effect 5 wires. Measure the resistance if the resistance between the case and any coil is half that between two wires then there you have your fifth wire.