In C#, how can I create a TextReader object from a string (without writing to disk)

Use System.IO.StringReader :

using(TextReader sr = new StringReader(yourstring))
{
    DoSomethingWithATextReader(sr);
}

Use the StringReader class, which inherits TextReader.

StringReader is a TextReader (StreamReader is too, but for reading from streams). So taking your first example and just using it to construct the CsvReader rather than trying to construct a StreamReader from it first gives:

TextReader sr = new StringReader(TextBox_StartData.Text);
using(CsvReader csv = new CsvReader(sr, true))
{
  DetailsView1.DataSource = csv;
  DetailsView1.DataBind();
}