Implementing IDisposable correctly on parent classes in C#

I have a class which implements the C# SerialPort which used to look like this:

public class AsyncSerial : IDisposable
{
    SerialPort newPort; //Parameters declared in my constructor
    //Constructor and other methods

    public void Dispose()
    {
        Dispose(true);
        GC.SuppressFinalize(this);
    }

    protected virtual void Dispose(bool disposing)
    {
        if(disposing)
        {
            this.Close();
            this.Dispose();
        }
    }
}

This throws up no warnings in code analysis (I got the code from MSDN as an example of how to do it properly).

Since I was only ever going to declare one SerialPort I figured I would make my class a child of SerialPort, but now I get warnings that I can't seem to fix.

public class AsyncSerial : SerialPort
{
    //Constructor and other methods

    public new void Dispose()
    {
        Dispose(true);
        GC.SuppressFinalize(this);
    }

    protected new virtual void Dispose(bool disposing)
    {
        if(disposing)
        {
            this.Close();
            this.Dispose();
        }
    }
}

Code warnings said the dispose methods should be new as they hide members, which I did, but I also get:

"Warning CA1063 Ensure that 'AsyncSerial.Dispose()' is declared as public and sealed"

Making it sealed means it has to be marked override (or I get compiler errors), making it override means it can be new, so I end up with:

Error CS0506 'AsyncSerial.Dispose()': cannot override inherited member 'Component.Dispose()' because it is not marked virtual, abstract, or override

I don't know the 'correct' way to implement disposing on a class with IDisposable in the parent class. Every example I find only fits having IDisposable as a base, but making my class

public class AsyncSerial : SerialPort, IDisposable
{
    //code
}

gives me a code analysis warning because SerialPort already implements IDisposable.

Should I just suppress the warning about Ensuring that 'AsyncSerial.Dispose()' is declared as public and sealed, or is there a correct way to do this which doesn't give code analysis warning.