With my hosting service its not possible to give anonym ftp connection due to security reasons, so I tried another alternative of public file sharing system such as dropbox.com and confgured the synapse to download that file from http protocol
Ok, so we can't use ftp because there is no anonymous access. Alright... Then for you're attempt of using dropbox.
You got a New_Bitmap_Image.bmp of 176. If you want to know what's happening you should rename that file to New_Bitmap_Image.txt and open it with an editor. You see something like this:
<html>
<head><title>301 Moved Permanently</title></head>
<body bgcolor="white">
<center><h1>301 Moved Permanently</h1></center>
<hr><center>nginx</center>
</body>
</html>
You've chosen the worst possible http-service for your purpose. Dropbox has multiple redirection schemes in place so you need to follow where you're send. That URL you gave is not a direct download link.
But do you really need dropbox in this instance?
You did say you had a web-hosting provider. They might not give you ananymous ftp access but they do provide just HTTP-access. So why don't you put that New_Bitmap_Image.bmp on there and use httpClient.HTTPMethod to get it from your own site?
It is possible to download it from dropbox but you would need to read the headers to know where you are redirected to. If putting the file on your own website (at your provider) is possible, it's much easier and your given code should work fine.