1. Is it in the Bible?
Yes. (most are references to sacrificial law of the old covenant
2. What do we believe it means?
If a believer would like to serve God (minister) he or she must be "covered". Any ministry must be "covered by the authority of another minister.
3. What does it really mean?
This teaching is simply the plot of Satan to hinder and limit Christians ministry.
If we studied ministry in the new testament Bible (which very few people do-!) we would see that ministry is a "gift given unto every one of us". Even the non-believer was created by God to serve Him (see psalm 68:18 and it's reference in ephesians 4) The ridiculous Bible reference this teaching is based on is this:
Nu 4:14 And they shall put upon it all the vessels thereof, wherewith they minister about it, even the censers, the fleshhooks, and the shovels, and the basons, all the vessels of the altar; and they shall spread upon it a covering of badgers' skins, and put to the staves of it.
Yes, we could infer that believers are to be "vessels of ministry"--but--to infer that the "covering" (of badger's skin-!) is a reference to functioning ministry "under the authority" of another ministry is a huge typological stretch!
But let's look at 2 other scriptures that speak of "covering"...
Eze 28:14 Thou art the anointed cherub that covereth; and I have set thee so: thou wast upon the holy mountain of God; thou hast walked up and down in the midst of the stones of fire.
(this is a reference to Satan, before he fell--his was a ministry of "covering")
Lu 8:16 No man, when he hath lighted a candle, covereth it with a vessel, or putteth it under a bed; but setteth it on a candlestick, that they which enter in may see the light.
(this is Jesus' teaching on "covering"--and is in reference to serving God. The "light" He refers to is the Gospel. Jesus says that no one should "cover" their ministry.)
Now, there is some truth that the Bible asks us to cooperate
with the ministry of other believers (see study on "submit").
But once again, the starting point that tradition gives us, which
says that ministry is authority over others, makes us misinterpret
the Bible. We seek to verify our wrong ideas by these kind of
erroneous typologies, which sound correct only because they are
in the bounds of our experience. Wrong experience.