How do I encrypt a java.util.Properties object (can be any size) using an RSA Public Key?

Question

This is the code I'm currently using. It uses the BouncyCastle Provider.

static
{
   Security.addProvider(new BouncyCastleProvider());
}

protected String encrypt(byte[] keyData, byte[] data) throws Exception {
   X509EncodedKeySpec keyspec = new X509EncodedKeySpec(keyData);
   KeyFactory kf = KeyFactory.getInstance("RSA", "BC");
   PublicKey pk = kf.generatePublic(keyspec);
   Cipher rsa =  Cipher.getInstance("RSA/None/OAEPWithSHA1AndMGF1Padding", "BC");
   rsa.init(Cipher.ENCRYPT_MODE, pk);
   byte[] output = rsa.doFinal(data);
   String result = base64EncodeBytes(output);
   return result;
}

I'm currently getting a

 java.lang.ArrayIndexOutOfBoundsException: too much data for RSA block
    at org.bouncycastle.jce.provider.JCERSACipher.engineDoFinal(Unknown Source)
    at javax.crypto.Cipher.doFinal(DashoA13*..)
    at Encryption.encrypt(RSAToken.java:60)