This bedroll provides a soft spot for your head out on the rugged range.
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—Store description
As with all similar items, the Bed Roll is not used in the game beyond unlocking a journal page. There is no specific connection between the item and the character who is unlocked.
The Bed Roll can be purchased from the General Store in Brimstone after completion of the mission "Railroaded". If not purchased, it is not available during subsequent visits to Brimstone.