When you are looking to the code of the NetRadio example:
In the "button1_Click" method (around line 390) you'll find the following code:
if ( BassTags.BASS_TAG_GetFromURL( _Stream, _tagInfo) )
In the respectice _tagInfo structure you'll find a "NativeTags" property, which let's you access all Tag-Values available.
To get the Bitrate you need to:
a) for WMA: look for an entry called: "Bitrate"
b) for ICY: look for an entry called: "icy-br"
Thats's how you might get the Bitrate for both WMA and SHOUTcast streams.