This is easy to do, you can render the report as a PDF, and save the resulting byte array as a PDF file on disk. To do this in the background, that's more a question of how your app is written. You can just spin up a new thread, or use a BackgroundWorker (if this is a WinForms app), etc. There, of course, may be multithreading issues to be aware of.
Warning[] warnings;
string[] streamids;
string mimeType;
string encoding;
string filenameExtension;
byte[] bytes = reportViewer.LocalReport.Render(
"PDF", null, out mimeType, out encoding, out filenameExtension,
out streamids, out warnings);
using (FileStream fs = new FileStream("output.pdf", FileMode.Create))
{
fs.Write(bytes, 0, bytes.Length);
}