Check out moons and especially new moons in the bible !
Well, to tell you the truth, I've never heard of a "Blue Moon" in the Bible. But, maybe you're not talking about a Blue Moon... and that's okay.
But, in mentioning the Moon (in context of the Blue Moon) -- we are talking about a "full moon" -- and in the Bible it seems that the relevance is on the New Moon, mostly -- which is the exact opposite (I would say) of the full moon.
The calendar and the Festivals of the Lord are timed according to the New Moon (or shortly thereafter, rather...) and not the way we think about it. Anyway..., I'm not sure of the relevance, in the Bible of "full moons" or "Blue Moons", but I am about the New Moons... :-)
1Sa 20:5 And David said unto Jonathan, Behold, to morrow [is] the new moon, and I should not fail to sit with the king at meat: but let me go, that I may hide myself in the field unto the third [day] at even.
1Sa 20:18 Then Jonathan said to David, To morrow [is] the new moon: and thou shalt be missed, because thy seat will be empty.
1Sa 20:24 So David hid himself in the field: and when the new moon was come, the king sat him down to eat meat.
2Ki 4:23 And he said, Wherefore wilt thou go to him to day? [it is] neither new moon, nor sabbath. And she said, [It shall be] well.
Psa 81:3 Blow up the trumpet in the new moon, in the time appointed, on our solemn feast day.
Isa 66:23 And it shall come to pass, [that] from one new moon to another, and from one sabbath to another, shall all flesh come to worship before me, saith the LORD.
Eze 46:1 Thus saith the Lord GOD; The gate of the inner court that looketh toward the east shall be shut the six working days; but on the sabbath it shall be opened, and in the day of the new moon it shall be opened.
Eze 46:6 And in the day of the new moon [it shall be] a young bullock without blemish, and six lambs, and a ram: they shall be without blemish.
Amo 8:5 Saying, When will the new moon be gone, that we may sell corn? and the sabbath, that we may set forth wheat, making the ephah small, and the shekel great, and falsifying the balances by deceit?
Col 2:16 Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath [days]: