You may use the white wire by making it unidentified. Paint or tabe it blue at every location the conductor is accessible. Until the 2006 code is enacted without amendments to tables 16 and 17 you may have a problem with the bonding conductor size.
A motor conductor is sized to the FLA of the motor say it is 14 amps. The conductor size is 14 X 1.25 or 17.5 amps. A number 12 BX is OK for the motor but the potential overcurrent protection presents a challenge. If you used the max breaker size of 35 amps the bonding conductor is too small at #14. An ISO type of bx with a full sized #12 bonding conductor would take care of this. Alternately you would need a # 8 cable to meet the min #10 bonding conductor from table 16. So why can I use a #12 ISO bx and need a #8 if I use a regular BX. The bonding conductor never needs to be larger than the circuit conductor. The 2006 code sizes the bonding conductor to the wire size appropriate for the load not to the OC device protecting the load. The cheapest solution now is ISO bx. Alternately an EMT run proximate to the motor with a short piece of flex and a #12 Bonding conductor in the flex works too. If the 2006 code is adopted without any amendments to table 16 and 17 then the #12 bx with taped or painted white wire works.