Uncirculates

I wouldn't recommend it. Once you have a few coins in there and start moving them around, they will get marked.

I have them in coin tubes from Littleton.

Oh I see, when you say bottles I was thinking something like mason jars or something similar. You were referring to the little tubes as jars. Just a confusion in the terminology.

Yes perfectly safe to put them right into the tubes for storage.

You should see the 'legal-ese' on sign posted at the Denver Mint Gift
Shop, regarding the never-circulated business strike Quarter and
Dollar coins sold there.

"Although these coins have never been circulated, they are not by
definition numismatic "Uncirculated" coins. Numismatic "Uncirculated"
coins are struck on different machinery, and have different handling
procedures within the U.S. Mint."
(as you can see on the Mint tour!)

To save SuperDave's head from exploding, how about:
"When I pick a BU coin from circulation, is it safe to put it into a
coin tube?"

Now that's different!

If it's a Carson City GSA grading MS65DMPL or higher; I would NOT put it in a tube!

It is entirely possible to find an uncirculated condition coin(MS60+) in circulation. A coin does not automatically become "circulated"(lower than MS60)through the act of monetary exchange or leaving the Mint for that matter, that is one of the biggest misconceptions floating around. A coin can pass through a few hands in commerce before the luster is disturbed and visible wear can be detected. This is especially true when you see a clerk break open a brand new roll and hand you a few of the coins as change- those coins are certainly uncirculated even though they have been used in commerce.

The terms "circulated" and "uncirculated" are nothing more than descriptors of physical wear, they have nothing to say about the amount of use in commerce. A coin can be naturally worn to PO-1 without ever being used in a monetary transaction or it can pass through a dozen hands without sustaining any wear. You just have to look at each coin on an individual basis, blanket statements do not apply.

I have two folders of Denver Mint State Quarters that are in MS-62
to MS-65 condition (by strict PCGS-type grading standards), all of
which were received in my change from retail transactions.

And that of course is the whole 'point' of those folders! Ironically,
the Territorial Quarters I'm proudest of are the AU coins, they prove
that at least some of these 2009 Quarters are getting a 'few miles'
on them (and that they're not just all getting hoarded out of
circulation while they're still in BU condition!)

My picayune definition of a 'circulation find' is 'received in change
from a retail transaction'; roll finds and coins found on the ground
or in CoinStar reject trays don't count (to me) as true 'circulation
finds'.