How to handle dirt caked in excavator bucket
If you can get the bucket clean and dry, a coat of paste wax will help, but for how long is debatable, and unknowable in practice unless you make the experiment.

Ideally wait for better weather, but that's difficult with rented equipment and/or deadlines. Be careful how hard you "bump on the ground" - it is possible to rather expensively break things with excess enthusiasm and the power of hydrualics. Sometimes just wiggling the bucket or boom in the air will get things to unload, with far less risk of damage.