Even though I have a phone number in my careers.stackoverflow profile:
That phone number isn't appearing in the replies I compose to potential employers:
Is this an option that can be turned on or is this simply a bug?
This is actually by design. When you apply to a job or an employer finds you in search, a small snapshot is taken of your contact details and it can not be changed from that point forward. Can you imagine how much more difficult an employers job would be if every resume they received had dynamic names, phone numbers, email addresses and city/state locations (which you can't see here but is also provided to employers)?
If you'd like to update the phone number for an employer after the contact details are set, the recommended way is to just send them another message with your phone number attached.