Obtaining Rolled Coins

The U.S. Mint website sells "P & D Two Roll Sets" of every one that comes out. The problem is, however, that you can't "go back" and buy the ones that you missed. They (Sets) are only available for a certain time......then they're gone. But knowing this, you can at least stay current with the ones that come out now.
FYI......there is a "premium" that the Mint charges for these rolls. ($32.95 + shipping and handling) So, I personally won't pay that kind of money for rolled coins......BU or not !

There would be "gift shops" outside or near each Mint facility like the one in Denver....but you cannot "order directly from those Mints". Writing a letter wouldn't produce you any rolls or anything else.
But.....going back to get "past" rolls....or a cheaper way to get "current" rolls....someone else will have to speak about that.

If you are looking for anything other than current year, the Mint isn't the place unless they have some of last years stock left. Auction sites will be your best bet, but you'll pay premiums.

If just simply looking for roll searching opps - then yes, go thru your bank and order boxes.