Honestly, the cheapest realistic option for a heavy street bench is almost always LTL freight with terminal-to-terminal pickup and delivery. A street bench is usually too heavy and too awkwardly shaped for standard parcel shipping once you factor in dimensional weight and oversize fees. You might get lucky with UPS or FedEx Ground if the bench is under about 150 pounds and can fit in a box, but most cast iron, steel, or concrete benches will blow past those limits fast.
The trick is to palletize the bench yourself. Get a sturdy standard 48x40 pallet, secure the bench with ratchet straps or metal brackets, and wrap the whole thing in stretch film. Carriers price LTL shipments by weight, freight class, distance, and accessorials. The fewer accessorials you add, the cheaper it gets. If you can drop the pallet off at a freight terminal and have the receiver pick it up at the destination terminal, you skip residential delivery fees, liftgate fees, and appointment charges. That terminal-to-terminal setup can easily save $100 to $250 compared with door-to-door residential service.
When I price these, I usually run quotes through a freight broker like FreightQuote, FreightCenter, or TSI because they pull rates from multiple LTL carriers such as FedEx Freight, Estes, Old Dominion, ABF, and TForce Freight. You can also list it on uShip and let smaller hotshot or partial-load haulers bid. Sometimes a hotshot driver with extra trailer space will move it for less than a national LTL carrier, especially for shorter regional runs.
For a typical 150 to 300 pound street bench on a pallet, I would expect LTL terminal-to-terminal to run roughly $150 to $400 depending on distance and freight class. Door-to-door residential delivery with a liftgate can jump to $400 to $800 or more. If someone offers blanket-wrap or white-glove delivery, it will be the most expensive route, so avoid it unless the bench is antique or fragile.
The biggest money-saving tips are simple: palletize it securely, know the exact weight and dimensions, ask about the correct freight class, choose terminal-to-terminal, avoid liftgate service if possible, and compare at least three quotes. Also check local auction houses, used office furniture movers, or regional couriers. Sometimes a local guy with a box truck will do it for less if the route is nearby.