Proper usage of "using" statement in base64 encode method
SRP  

Your method is responsible of to many things, like  


reading from a file
writing to a file  
converting to base64  


So I would suggest to add some more methods  

public static bool ConvertToBase64(string inputFile, string outputFile)
{
    try
    {
        byte[] input = System.IO.File.ReadAllBytes(inputFile);
        byte[] base64 = ConvertToBase64(input);
        System.IO.File.WriteAllBytes(outputFile,base64);
        return true;
    }
    catch(Exception)
    {
        return false;
    }
}

private byte[] ConvertToBase64(byte[] input)
{


}


As already stated in the comment, the inner try..catch statements are useless. Your outer try..catch would handle the exceptions in the same way.  

About the using statements  

If you don't need them, don't use them. As you are reading/writing to/from a file, you can just use the above methods, which internally using a using statement. Always use the right tool to do the job.  

If you need to use using statements, you can also stack them like  

using (disposable1)
using (disposible2)
{

}


Comments  

Don't use comments to describe what you are doing, but why you are doing something. Especially if it is crystal clear what you are doing like  

//Buffers for read/write operations
Byte[] outputBuffer = new byte[base64Transform.OutputBlockSize];
Byte[] inputBuffer = new byte[inputFileStream.Length];


this comment is just useless.

Magic numbers  

As you need a comment to describe  

if (inputOffset % 19 == 0)  


you should better use a const for that 19 (but don't ask me how to name it)  

If you still want the inner try..catch you can simply use catch(Exception) as there is no need for ex.  

Otherwise your code looks good. The naming of your fields is also meaningful.