The text that it shows when you use the export (the 13 x 4 digits) IS the private key... it is just in a "Private Key WIF Compressed" format. This is 52 characters (13x4 = 52)... base58 and starts with a 'K' or 'L.
To double check this, I've grabbed a copy of the Bither, fired it up and generated a test wallet that has the address: 1AWnnam3v12UUbXW3LndYvgZKfYkNQGU4a
The export gives me a value of: L3AWRHyjowHCkdmffUyjqvgAejfzQ1xrXEzsBJ7oJr5iSpFrexDU (Note: You need to remove all the spaces)
Then I went to bitaddress.org and under "Wallet Details"... copied the value into the "Private Key" box... and hit "view details"... it shows:
Private Key WIF
51 characters base58, starts with a '5'
5KAQRzKHx3L5UZM68p7xvgMChiqi6fjZWxjZfanVcmCVRSe6sGr
Private Key WIF Compressed
52 characters base58, starts with a 'K' or 'L'
L3AWRHyjowHCkdmffUyjqvgAejfzQ1xrXEzsBJ7oJr5iSpFrexDU
Private Key Hexadecimal Format (64 characters [0-9A-F]):
B16070710D0BD2CE966B4674C824FBE9F09A7F9613D68757B5223EF79E3D6DB7
IMPORTANT: DO NOT copy your actual exported private key to bitaddress.org and run tests there!! That could potentially expose your private key!!If you need to convert it from WIF compressed to WIF, you will need to do it yourself, preferably on an offline computer... You will need to read
about Wallet Import Format, WIF and also
Base58Check EncodingYou could also download the offline version of bitaddress.org from their website and try that (click the "zip" link in the bottom left hand corner)... I absolutely NO guarantees that the code is safe... use it at your own risk!