I can't actually try this right now, but here is a possibility. You can get the session id in your CLR like so...
using (SqlConnection cn = new SqlConnection("context connection=true;"))
{
cn.Open();
SqlCommand cmd = new SqlCommand("SELECT @@SPID", cn);
int spid = Convert.ToInt32(cmd.ExecuteScalar());
cn.Close();
}
Then, try to use the query shown in the accepted answer for this SO question...