You can use the overload of
String.Split[
^] which takes a StringSplitOptions:
string[] bits = text.Split(new[] {' '}, StringSplitOptions.RemoveEmptyEntries);
To avoid creating a char array on each call, you can use:
private static readonly char[] SplitSeparators = {' '};
...
string[] bits = text.Split(SplitSeparators,
StringSplitOptions.RemoveEmptyEntries);