The bishop's phone number listed on the Maps application on LDS.org (aka Meetinghouse Locator) is the bishop's home phone number as listed in CDOL. One of the bishops in our stake doesn't have a home phone number in CDOL (but he does have a mobile and work number) and his ward has no phone number listed for the bishop on Maps on LDS.org.
You can change that number by signing into CDOL, clicking on your name (which you can find by looking at your ward), and then clicking Edit Assignment.
The particular request here is a bit tricky, since you'd have to change your home phone number in CDOL to a number that is not your home phone number, so there would no longer be a home phone number listed in CDOL. But CDOL does let you enter a "Home Phone #2", which I'm guessing would not be used by the Maps application, but would most likely still be visible to other Church leaders who tried to contact you via CDOL.
Questions that can benefit the larger community should be asked in a public forum, not a private message.