Check your data in the DB: almost certainly you have saved it wrong.
If I try your code:
String ClientSigImg;
String ClientSigImg1;
ClientSigImg = @"data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7";
ClientSigImg1 = ClientSigImg.Split(',')[1];
string base64 = ClientSigImg1;
byte[] imageBytes = Convert.FromBase64String(base64);
It works - and I get an array of 43 bytes.
So I would suspect that what you think is valid data in your DB is not: at least one entry does not have a comma. So the Split returns an array of one string, and your indexer fails giving you the "Index was outside the bounds of the array" exception.