Enable the move_objects on code. Then, pick up the mailbox and erase it. Bills cannot be delivered if you do not have a mailbox. However, no one will know where you live. Visitors will appear at your house, but just stand there. You also will not be able to greet them.
If you delete your mailboxes it may cause complications such no more pizza, carpools, etc. Try this instead. Click the mailbox and choose "Get mail". Your Sim will get the mail, then will set it down somewhere. Enable the move_objects on code. Then, click buy mode, pick up the mail with the hand icon, then press DELETE or choose the "Delete mail" option at the bottom of the screen.
Use the following trick to pay your bills, but cost you nothing. Tell your Sim to pay the bill as soon as he or she walks into the same room as the bill. Pause and save the game, then enable the move_objects on code. Delete your Sim, then revive him while the game is still paused. Resume the game and tell your Sim to pay the bill. The bill should be reduced to 0 Simoleons.
Save the game, then enable the move_objects on code. When your Sim has all of the bills in his hand, delete your Sim in buy mode. Then, return to live mode. Click on your Sim's picture. Your Sim will reappear, but your bills will not.
Have your Sim pay bills. Make sure the bills are in the white envelope and that your Sim in walking to the mailbox. Quickly go to buy mode and buy an object, making sure that you use more than you owe on the bills. Then, return to live mode. Your Sim will pay the bill even if there is 1 Simolean remaining. To get your money back, go back to buy mode and sell the object. You will keep all your money.
Buy a fireplace and place it in an empty room. Note: This may work better if you sacrifice an 30 Simoleon trash can to start the fire, since that is usually much cheaper than the bills. It may or may not work without it -- this was tested when they were on a table. Place your bill(s) on the left side or in front of the fireplace. Have a Sim start a fire. Note: If any Sims die, exit without saving.