This can be easily accomplished at the General Store in Edgewater and also works at any vendor or vending machine. Save your game and then unequip all weapons, armor and consumables prior to entering the trade screen and then sell all your items to the vendor. Next, switch to the Buy screen and use the buyback tab on the far right to buy the items for the same price you sold them for. You can buy and sell the same items multiple times and each time you sell it will count towards the 10,000 bits.
The more items you have in your inventory the quicker this will be, but could be done 1 bit at a time. If you have 1,000 bits worth of items you would need to repeat 10 times to get the 10,000 needed for the achievement