Here's the code I used. It assumes the source is in the same folder as the executable, and includes running BibTeX if you need it (just exclude the second process if needed).
string filename = "<your LaTeX source file>.tex";
Process p1 = new Process();
p1.StartInfo.FileName = "<your path to>\pdflatex.exe";
p1.StartInfo.Arguments = filename;
p1.StartInfo.WindowStyle = ProcessWindowStyle.Hidden;
p1.StartInfo.RedirectStandardOutput = true;
p1.StartInfo.UseShellExecute = false;
Process p2 = new Process();
p2.StartInfo.FileName = "<your path to>\bibtex.exe";
p2.StartInfo.Arguments = Path.GetFileNameWithoutExtension(filename);
p2.StartInfo.WindowStyle = ProcessWindowStyle.Hidden;
p2.StartInfo.RedirectStandardOutput = true;
p2.StartInfo.UseShellExecute = false;
p1.Start();
var output = p1.StandardOutput.ReadToEnd();
p1.WaitForExit();
p2.Start();
output = p2.StandardOutput.ReadToEnd();
p2.WaitForExit();
p1.Start();
output = p1.StandardOutput.ReadToEnd();
p1.WaitForExit();
p1.Start();
output = p1.StandardOutput.ReadToEnd();
p1.WaitForExit();
Yes, this could be cleaned up a little, and certainly without the call to BibTeX could just be called in a loop (3 times is the recommended number to make sure all the references are correct). Also, there's no exception handling, so you might want to add try / catch blocks around the process calls, etc.