How to check wether a CloudBlobDirectory exists or not?

In blob storage, directories don't exist as an item by themselves. What you can have is a blob that has a name that can be interpreted as being in a directory. If you look at the underlying REST API you'll see that that there's nothing in there about directories. What the storage client library is doing for you is searching for blobs that start with the directory name then the delimiter e.g. "DirectoryA/DirectoryB/FileName.txt". What this means is that for a directory to exist it must contain a blob. To check if the directory exists you can try either:

var blobDirectory = client.GetBlobDirectoryReference("Path_to_dir");
bool directoryExists = blobDirectory.ListBlobs().Count() > 0

or

bool directoryExists = client.ListBlobsWithPrefix("DirectoryA/DirectoryB/").Count() > 0

I'm aware that listing everything in the directory just to get the count isn't that great an idea, I'm sure you can come up with a better method.