asterisk 6 7
If this phone number is a contact in your phone, then on my phone I'm able to precede the phone number in the contact entry with the asterisk 6 7 so that my ID is blocked every time I call that person.
MojaveMoon's solution will work if there is only one person you want to block your ID from; if you want to block your caller ID from everyone, you can go to your account online, go to Change Features, and scroll down till you see Caller ID block. Instructions say that once this is activated, you can dial *82 before any # you WANT to display your number to, but all others will be blocked.
If you are on a Family share plan, the account owner needs to log in and choose your line to activate this feature.