Using SecureString

You could use Linq:

"fizzbuzz".ToCharArray().ToList().ForEach(p => secureString.AppendChar(p));

Just use NetworkCredential. It has the conversion logic built-in.

SecureString ss = new NetworkCredential("", "fizzbuzz").SecurePassword;

As others have noted, all of these techniques strip the security benefits of SecureString, but in certain situations (such as unit tests) this may be acceptable.

Update:

As noted in the comments, NetworkCredential can also be used to convert a SecureString back to a string.

string s = new NetworkCredential("", ss).Password;