The bottle is simple glass shader and the desert is a deformed plane mesh with thickness. But as we can see, the bottle buried gives a really weird look of deep black hole. I want to get rid of this black hole with filling it with sand. How can I achieve this?
The first step is to make a cavity in the sand. I can't tell from your image if you've done that or not. I used the Boolean Modifier (to save time) in order to make this hole the same size as the bottle, but you can also model it which would be more beneficial in the long run:
Adding more bounces to any of the Light Path inputs will result in longer render times and has diminishing returns. I would set the Transmission bounces to around "5" since there's little difference beyond that:
What you really need is a node setup that will allow you to adjust how much shadow is cast on the ground and in the hole. This node tree has been around the block a few times and it's still just as effective. Adjust the Multiply factor to remove shadow caused by the Glass Shader. Zero is full shadow, one is no shadow:
Here is the final with a factor of 0.8: