The ReportDocument has a method called ExportToStream. Use the ExportFormatType.HTML40 option as the parameter.
Here's some sample code that reads the output into a byte array. You can use this to eventually convert it to text.
byte[] buffer = null;
var rpt = new ReportDocument(); // your report object would go here instead.
using (var sr = new StreamReader(rpt.ExportToStream(ExportFormatType.HTML40)))
{
buffer = new byte[sr.BaseStream.Length];
sr.BaseStream.Read(buffer, 0, buffer.Length);
rpt.Close();
rpt.Dispose();
rpt = null;
}