Since you are bringing it in as a string this is actually kind of easy.
string StartTime = ((TextBox)TestDV.FindControl("txtBST")).Text.ToString();
DateTime dt = new DateTime();
try { dt = Convert.ToDateTime(StartTime); }
catch(FormatException) { dt = Convert.ToDateTime("12:00 AM"); }
StartTime = dt.ToString("HH:mm");
So you bring in your string, and convert it to a date. if the input is not a valid date, this will default it to 00:00. Either way, it gives you a string and a DateTime object to work with depending on what else you need to do. Both represent the same value, but the string will be in 24-Hour format.
Cheers!!