In that case, if you're looking for speed then an I2C EEPROM isn't the best of choices.

I have no idea how slow the bit-banged I2CREAD is (probably pretty slow).
A 24C256 isn't all that slow, but you're going to be limited to about 400KHz using the pic's MSSP hardware.
That means a random read operation works out to something like 120us/byte @ 400KHz.

A faster choice would be an SPI EEPROM like a 25LC512. There you'll probably be able to get the MSSP to run at 8MHz,
which would speed up the random read to about 5-10us/byte.

If you can read more than 1 byte at a time then the operations are a bit faster, but Henrik's suggestion of using program memory would be faster.