A simple method of hiding a number on a cellphone bill is to activate caller ID block on that number. If caller ID block is activated on a particular number, then it will appear as "Private" or "Withheld" on the caller ID of any phone that is rang from that phone number. In addition to this, the restricted phone number will also be hidden on the cellphone bill of the person who is called, and will appear as "Unavailable" in the call detail section of the bill.
Activate caller ID block permanently on your phone. Contact your phone service provider and request them to permanently activate caller ID block on your phone.
Activate caller ID block only for one call. Press "*67" followed by the phone number at which you do not want to disclose your identity. Your phone number will appear as "restricted" only for this call.
Use a pay phone to make the call. This will also prevent your phone from showing on the called party's phone bill.